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# What does InternalInheritedBlock do?

What does the function InternalInheritedBlock do? How is it different from the regular Block?

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Popular use of this function started with Daniel's MathGroup post: forums.wolfram.com/mathgroup/archive/2010/Dec/msg00710.html –  Mr.Wizard May 25 '13 at 15:21

InternalInheritedBlock (IIB) is similar to Block, except that it preserves the original definition of the function being passed to it. The function can then be modified as we wish inside the IIB without affecting the external definition.

Let's see how Block works first:

f[x_] := x
Block[{f},
Print@DownValues[f];
f[x_, y_] := x y;
Print@DownValues[f];
];
Print@DownValues[f];

(* {} *)
(* {HoldPattern[f[x_, y_]] :> x y} *)
(* {HoldPattern[f[x_]] :> x} *)

You notice that the original definition of f is not available inside the Block. On the other hand, look at what IIB does:

f[x_] := x
InternalInheritedBlock[{f},
Print@DownValues[f];
f[x_, y_] := x y;
Print@DownValues[f];
];
Print@DownValues[f];

(* {HoldPattern[f[x_]] :> x} *)
(* {HoldPattern[f[x_]] :> x, HoldPattern[f[x_,y_]] :> x y} *)
(* {HoldPattern[f[x_]] :> x} *)

The original definition of f is available inside its scope, and new definitions are added to the existing ones (as is the usual behaviour), unless you explicitly clear them.

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Search results

Search: MSC category 14T05 ( Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] )

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1. CJM 2012 (vol 65 pp. 120)

Francois, Georges; Hampe, Simon
 Universal Families of Rational Tropical Curves We introduce the notion of families of $n$-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical varieties into the moduli space of $n$-marked abstract rational tropical curves $\mathcal{M}_{n}$. Keywords:tropical geometry, universal family, rational curves, moduli spaceCategories:14T05, 14D22

2. CJM 2011 (vol 64 pp. 845)

Helm, David; Katz, Eric
 Monodromy Filtrations and the Topology of Tropical Varieties We study the topology of tropical varieties that arise from a certain natural class of varieties. We use the theory of tropical degenerations to construct a natural, multiplicity-free'' parameterization of $\operatorname{Trop}(X)$ by a topological space $\Gamma_X$ and give a geometric interpretation of the cohomology of $\Gamma_X$ in terms of the action of a monodromy operator on the cohomology of $X$. This gives bounds on the Betti numbers of $\Gamma_X$ in terms of the Betti numbers of $X$ which constrain the topology of $\operatorname{Trop}(X)$. We also obtain a description of the top power of the monodromy operator acting on middle cohomology of $X$ in terms of the volume pairing on $\Gamma_X$. Categories:14T05, 14D06

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# Mahalanobis Distance Python

Matching Procedures Mahalanobis distance matching (MDM) and propensity score matching (PSM) are built on speciﬁc notions of distance between observations of pre-treatment covariates. Mahalanobis distance is a metric used to compare a vector to a multivariate normal distribution with a given mean vector ($$\boldsymbol{\mu}$$) and covariance matrix ($$\boldsymbol{\Sigma}$$). affiliations[ ![Heuritech](images/logo heuritech v2. The dimension of the embedding space is the product of the number 34 of levels of all the variables. They are extracted from open source Python projects. A distance metric. A smaller Tg value generates more components. The associated norm is called the. In the following we are assuming that you have correctly installed Plotly for Python. Clustering analysis or simply Clustering is basically an Unsupervised learning method that divides the data points into a number of specific batches or groups, such that the data points in the same groups have similar properties and data points in different groups have different properties in some. I am writing it in conjunction with my book Kalman and Bayesian Filters in Python, a free book written using Ipython Notebook, hosted on github, and readable via nbviewer. We consider semi-supervised learning, learning task from both labeled and unlabeled instances and in particular, self-training with decision tree learners as base learners. To analyze traffic and optimize your experience, we serve cookies on this site. In this section we provide an overview of the spectrum of matching methods available. All pixels are classified to the closest ROI class unless you specify a distance threshold, in. Planning and Decision Making. Wminkowski, Seuclidean Distance, or Mahalanobis Distance. The goal of metric learning techniques is to improve matters by incorporating side information, and optimizing parametric distance functions such as the Mahalanobis distance [7, 12, 30, 34, 36]. Download Open Datasets on 1000s of Projects + Share Projects on One Platform. pop( key, 0 ) Write a line like this (you'll have to modify the dictionary and key names, of course) and remove the outlier before calling featureFormat(). If you are interested in performance and want to speed some part of your code, you have the possibility to move it in a Cython module. I am looking for NumPy way of calculating Mahalanobis distance between two numpy arrays (x and y). The Mahalanobis distance is a generalization of the Euclidean distance, which addresses differences in the distributions of feature vectors, as well as correlations between features. An example to show covariance estimation with the Mahalanobis distances on Gaussian distributed data. GPyOpt: A Bayesian optimization framework in Python. developed as a viable alternative. Image similarity is the distance between the vectors of two images. The concept of distance between two samples or between two variables is fundamental in multivariate analysis - almost everything we do has a relation with this measure. Depending on the data sets you are dealing with there is a high probability that you will need to perform some type of distance computation or similarity computation. Finally, Rosenbaum (1989) reports parenthetically. current-mirror input. Hi, thank you for your posting! I wonder how do you apply Mahalanobis distanceif you have both continuous and discrete variables. Mahalanobis distance g The Mahalanobis distance can be thought of vector distance that uses a ∑i-1norm n ∑-1can be thought of as a stretching factor on the space n Note that for an identity covariance matrix (∑i=I), the Mahalanobis distance becomes the familiar Euclidean distance g In the following slides we look at special cases of the. ZD Javier Gonzalez. Once populated, we can sort the list by distance, take the first k values from that list, find the most popular, and we have our answer!. Moment estimates may be used i. mahalanobis extracted from open source projects. • Language used: Python. The ﬁnal method seems to be com pletely new and. Questions: I have computed a test statistic that is distributed as a chi square with 1 degree of freedom, and want to find out what P-value this corresponds to using python. The first section discusses face recognition applications with examples. Rayleigh quotient. Robust covariance estimation and Mahalanobis distances relevance¶ An example to show covariance estimation with the Mahalanobis distances on Gaussian distributed data. Now rerun the code, so your scatterplot doesn't have this outlier anymore. Using Mahalanobis Distance to Find Outliers. If this method serves as a signi cant improvement over its competitors, then it will provide a useful tool for. Finally, add to your samples so that the mean is. Principles of the Analysis of Variance. DAT) Y1LABEL Minkowski Distance MINKOWSKI DISTANCE PLOT Y1 Y2 X Program 2: set write decimals 3 dimension 100 columns. Also, the choice of the distance function is subjective. Comparison: if you study the following figure carefully, you will find that different distance measures led to different clusters formation. The following are code examples for showing how to use scipy. 马氏距离(Mahalanobis distance)和欧氏距离(Euclidean distance ) 昨天在网上发现了一个非常方便的天气API，就用Python试着用了一下。. A multivariate outlier is a combination of unusual scores on at least two variables. The first section discusses face recognition applications with examples. Coding K-Nearest Neighbors Machine Learning Algorithm in Python. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. Cosine Distance Let’s compare two different measures of distance in a vector space, and why either has its function under different circumstances. Identifying and Addressing Outliers – – 83. The 2012 IEEE Change Detection Workshop (CDW-2012) is now concluded. Outliers in data can distort predictions and affect the accuracy, if you don’t detect and handle them appropriately especially in regression models. So, I set up Anaconda(3) on my Windows 8 computer, it worked without problems. Questions: I have computed a test statistic that is distributed as a chi square with 1 degree of freedom, and want to find out what P-value this corresponds to using python. 'cityblock' — City block distance. There are multiple metrics for deciding the closeness of two clusters like squared Euclidian distance, Manhattan distance, Mahalanobis distance etc. Moment estimates may be used i. Interpretation of Mahalanobis distance The Mahalanobis distance between two multivariate quantities x and y is If the covariance matrix is k. By clicking or navigating, you agree to allow our usage of cookies. Both types of outliers can influence the outcome of statistical analyses. Elder 8 Orthonormal Form Since it is used in a quadratic form, we can assume that Σ−1 is symmetric. Pattern Analysis and Machine Intelligence, vol. 标签 Python 马氏距离 Mahalanobis Distance 巴氏距离 欧氏距离 闵氏距离 计算距离 距离计算 什么是马氏距离 欧氏距离 Mahalanobis. Then partitioned as the distance increases. The stan-dard method for multivariate outlier detection is robust estimation of the parameters in the Mahalanobis distance and the comparison with a critical value of the ´2 distribu-tion (Rousseeuw and Van Zomeren, 1990). If this method serves as a signi cant improvement over its competitors, then it will provide a useful tool for. Raspberry Pi Camera + Python + OpenCV (Day2) 1. mahalanobis(u, v, VI) [source] ¶ Computes the Mahalanobis distance between two 1-D arrays. The associated norm is called the Euclidean norm. Implement Radial Basis function (RBF) Gaussian Kernel Perceptron. The most common is Euclidean Distance, which is the square root of the sum of the squared differences between corresponding vector component values. By clicking or navigating, you agree to allow our usage of cookies. ) and a point Y ( Y 1 , Y 2 , etc. The intuition behind the Mahalanobis is it measures how many standard deviations an given point is away from the mean. The usage is intuitive, add the distance measure node of your choice to the workflow, connect the input port to the data set which is also used in the distance measure using node (e. However, outliers do not necessarily display values too far from the norm. Illustration for n=3, repeated application of the Pythagorean theorem yields the formula In mathematics , the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. The test files in this directory also give you a basic idea of use, albeit without much description. examine the minimum Mahalanobis distance among observations that are not in the subset d min. Once a distance measure has been selected, the next step is to use that distance in doing the matching. 45 Expectation of Mahalanobis square distance of normal random variables. These models are very easy to interpret. that of Mahalanobis distance which is known to be useful for identifying outliers when data is multivariate normal. With CVM distance measures like the Mahalanobis distance are used to calculate similarity of two individuals in terms of covariate values and the matching is done on these distances. In this section we provide an overview of the spectrum of matching methods available. Mahalanobis all d> 0 distance between groups weighted by within-group dispersion: metric Distance measures can be categorized as metric, scmimetric. It might be a good idea to use the Mahalanobis Distance if your data shows high correlation between attributes or if your data is in different units or scales. mahalanobis¶ scipy. Usually, standard distances, like euclidean distance, are used to measure this similarity. The algorithm aims at minimiz-. The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. First, it allows you to view. In this regard, it differs from a one-way ANOVA, which only measures one dependent variable. Finally, Rosenbaum (1989) reports parenthetically. Like all buzz terms, it has invested parties- namely math & data mining practitioners- squabbling over what the precise definition should be. 아래 그림의 세 경로는 맨해튼 거리 기준으로는 같은 거리입니다. If this method serves as a signi cant improvement over its competitors, then it will provide a useful tool for. TL;DR: How can write a node that subscribes to topics under customized messages that's published from a bag when I don't have access to the definition of the customized messages (the. That's very common. Consultez le profil complet sur LinkedIn et découvrez les relations de Jean-Malo, ainsi que des emplois dans des entreprises similaires. My calculations are in python. Stackoverflow mahalanobis numpy question. The ﬁnal method seems to be com pletely new and. Data Science for Finance. The basis for multivariate outlier detection is the Mahalanobis distance. The formula for this distance between a point X ( X 1 , X 2 , etc. Curator's Note: If you like the post below, feel free to check out the Machine Learning Refcard, authored by Ricky Ho!. I need the distance between the means of two MVN distributions, not the distance from an observation to the center of a cloud of points. mahalanobis(u, v, VI) [source] ¶ Computes the Mahalanobis distance between two 1-D arrays. sum((x-y)**2)) a = numpy. Last revised 30 Nov 2013. But the Mahalanobis Distance also takes into account how far the Height, Score, and Age values are from each other. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. Then partitioned as the distance increases. Intuitively, we might think of a cluster as comprising a group of data points whose inter-point distances are small compared with the distances to points outside of the cluster. When the covariance. What is the Mahalanobis distance? The Mahalanobis distance (MD) is the distance between two points in multivariate space. Mahalanobis Distance. Use Mahalanobis Distance. Hamming distance), not the distance between coordinates (which is measured in Pixels)! @param mask Mask specifying permissible matches between an input query and train matrices of descriptors. There are many different ways to measure the distance between two vectors. untuk mempelajari hubungan antara sudut dan jarak. The formula for this distance between a point X ( X 1 , X 2 , etc. The app allows you to see the trade-offs on various types of outlier / anomaly detection algorithms. In the proposed method, a judging index is defined as the square of the Mahalanobis distance from the observation to its prediction. 'chebychev' — Chebychev distance, which is the maximum coordinate difference. Curator's Note: If you like the post below, feel free to check out the Machine Learning Refcard, authored by Ricky Ho!. In a particular subset of the data science world, “similarity distance measures” has become somewhat of a buzz term. Elder 8 Orthonormal Form Since it is used in a quadratic form, we can assume that Σ−1 is symmetric. Python Math: Exercise-79 with Solution. For new samples, the Mahalanobis distance to each of the class centroids is computed and can be used as an additional predictor. Distance Metric Learning algorithms try to learn an optimal distance from the data. Designed a multiple and logistic regression model for ‘Internet Users’ using ‘Education’ and ‘Mobile Users,’. It differs fromEuclidean distance in that it takes into. Mahalanobis distance is the distance between two N dimensional points scaled by the statistical variation in each component of the point. Explore Popular Topics Like Government, Sports, Medicine, Fintech, Food, More. Mahalanobis distance. that of Mahalanobis distance which is known to be useful for identifying outliers when data is multivariate normal. Mahalanobis in 1936. We talked before about the Cartesian coordinate system. Consequently, when two classes have similar means but different. The Mahalanobis distance measures the distance from each point in multivariate space to the overall mean or centroid, utilizing the covariance structure of the data. This metric is the Mahalanobis distance. The basis for multivariate outlier detection is the Mahalanobis distance. The algorithm can be seen as a generalization of the euclidean distance, but normalizing the calculated distance with the variance of the points distribution used as fingerprint. In the original project, "Health and Local Development: a progress review towards the millennium goals with relation to health in the Brazilian cities which develop. A distance metric. Color Supported Generalized-ICP 0 Michael Korn, Martin Holzkothen and Josef Pauli Lehrstuhl Intelligente Systeme, Universitat Duisburg-Essen, 47057 Duisburg, Germany¨. Hi, thank you for your posting! I wonder how do you apply Mahalanobis distanceif you have both continuous and discrete variables. Springer, 2014. A function for transforming a matrix from its Euclidean space to its Mahalanobis the Mahalanobis distance md1 <-sqrt Python'), and 'Kotlin. The workshop opening talk and challenge results and findings can be found here: CDW-2012 overview. Absence of multivariate outliers is checked by assessing Mahalanobis Distances among the participants. Flexible Data Ingestion. Where the Hamming distance between two strings of equal length is the number of positions at which the corresponding character are different. Other authors suggest that any “large” D i should be. array((1,2,3)) b = numpy. It is the most obvious way of representing distance between two points. Returns the squared Mahalanobis distance of all rows in x and the vector mu = center with respect to Sigma = cov. Here is what I started out with: #!/usr/bin/python import numpy as np def euclidean_dist_square(. There are multiple metrics for deciding the closeness of two clusters like squared Euclidian distance, Manhattan distance, Mahalanobis distance etc. This post was written for developers and assumes no background in statistics or mathematics. Once a distance measure has been selected, the next step is to use that distance in doing the matching. 2 When two items differ, the distance is positive. in the K-Means algorithm the Mahalanobis distance metric was used to capture the variance structure of the clusters. We use various classification rules, such as linear, quadratic, logistic, k nearest neighbor (k-NN), and k rank nearest neighbor (k-RNN) rules and compare the performances. This is the same as Euclidean distance. Mahalanobis’ Distance is regard distance between X and Y as same if X and Y have existed over the same ellipse. I am writing it in conjunction with my book Kalman and Bayesian Filters in Python, a free book written using Ipython Notebook, hosted on github, and readable via nbviewer. This method is based on a k-means algorithm in which the distance between the curves is measured with a metrics that generalizes the Mahalanobis distance in Hilbert spaces, considering the correlation and the variability along all the components of the functional data. There are many different ways to measure the distance between two vectors. The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. The results are slightly different than the one shown in Section 9. This metric is the Mahalanobis distance. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. An interesting use of the covariance matrix is in the Mahalanobis distance, which is used when measuring multivariate distances with covariance. Theory of Mahalanobis Distance Assume data is multivariate normally distributed (d dimensions) Appl. Author: PEB. is the Mahalanobis distance, defined as MD2 = R(x;⎯x, Γ) for each point xi, where⎯x is the sample mean of the data set, and Γ is the sample covariance matrix. Introduction¶. If you are interested in performance and want to speed some part of your code, you have the possibility to move it in a Cython module. Then aggregating them as the distance decreases. Also known as rectilinear distance, Minkowski's L 1 distance, taxi cab metric, or city block distance. Here is what I started out with: #!/usr/bin/python import numpy as np def euclidean_dist_square(. Last revised 30 Nov 2013. Let's consider sample dataset:. When a Euclidean distance is desired, the y input is connected.  How to compute the cumulative distribution functions and the percent point functions of various commonly used distributions in Excel, R and Python. Created a new method for running test simulations on-demand using system-level programming in C. dat y1 y2 y3 y4 skip 0. I recently blogged about Mahalanobis distance and what it means geometrically. Written by Peter Rosenmai on 25 Nov 2013. With CVM distance measures like the Mahalanobis distance are used to calculate similarity of two individuals in terms of covariate values and the matching is done on these distances. Options Distance Function Select distance function to use. is the Mahalanobis distance, defined as MD2 = R(x;⎯x, Γ) for each point xi, where⎯x is the sample mean of the data set, and Γ is the sample covariance matrix. , in the RX anomaly detector) and also appears in the exponential term of the probability density. It takes into account the variance of each variable, and the covariance. Mahalanobis distance g The Mahalanobis distance can be thought of vector distance that uses a ∑i-1norm n ∑-1can be thought of as a stretching factor on the space n Note that for an identity covariance matrix (∑i=I), the Mahalanobis distance becomes the familiar Euclidean distance g In the following slides we look at special cases of the. There are many different ways to measure the distance between two vectors. 1 Mahalanobis Distance (MD i) Mahalanobis distance (MD) is a statistical measure of the extent to which cases are multivariate outliers, based on a chi-square distribution, assessed using p <. diva-portal. It is often used for data scattered around an origin, as it is biased for measures around the origin and very sensitive for values close to zero. Once a distance measure has been selected, the next step is to use that distance in doing the matching. multivariate techniques and parametric vs. The function is part of my distance module and is called distance. There is no built-in distance for this (that i know of) Here's a list. Characterization through SVD and eigenanalysis. Linear Distance – First perform a linear mapping to project the data into some space, and then evaluate the pairwise data distance as their Euclidean distance in the projected space – Generalized Mahalanobis distance • • If M is symmetric, and positive definite, D is a distance metric;. Minitab displays a reference line on the outlier plot to identify outliers with large Mahalanobis distance values. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. The complete source code in R can be found on my GitHub page. This method is based on a k-means algorithm in which the distance between the curves is measured with a metrics that generalizes the Mahalanobis distance in Hilbert spaces, considering the correlation and the variability along all the components of the functional data. He is best remembered for the Mahalanobis distance, a statistical measure, and for being one of the members of the first Planning Commission of free India. The value of $\alpha$ is simply the threshold Mahalanobis distance where you decide whether your smallest Mahalanobis distance is indeed a measurement of a landmark in your map, or it is actually a new landmark. Intuitively, you could just look at how far v (66, 640, 44) is from the mean of the dataset (68. Python is a great language to solve several problems. • Validated results via statistical measures, e. In the following we are assuming that you have correctly installed Plotly for Python. class: center, middle # Class imbalance and Metric Learning Charles Ollion - Olivier Grisel. This week, I improved my implementation of Mahalanobis distance a bit. The issue with using Mahalanobis distances is that the accuracy of the distance is sensitive to initialization. In our daily life, we group. Mahalanobis in 1936. Finally, add to your samples so that the mean is. There appears to be a misconception here. It only takes a minute to sign up. To examine prescores on the two constructs of motivation and job satisfac-tion, Dr. Euclidean ini biasanya diterapkan pada 2 dimensi dan 3 dimensi. Clearly, the Mahalanobis distance relies on classical location and scale estimators. A more sophisticated technique is the Mahalanobis Distance, which takes into. As we did with the calculation of the distance, your code will run much much faster!. The Mahalanobis distance aims to do essentially the same thing, find out how far any given point is away from the bulk of the data points. After going through this video- you will know What is Mahalanobis Distance? Where it is used in linear discriminant analysis? Issues with Euclidian distance An intuitive understanding of. 'cityblock' — City block distance. When you are dealing with probabilities, a lot of times the features have different units. He is best remembered for the Mahalanobis distance, a statistical measure, and for being one of the members of the first Planning Commission of free India. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. 4/ or its scaled version dsc min. 33 (no units). These are Euclidean distance, Manhattan, Minkowski distance,cosine similarity and lot more. The Mahalanobis distance is similar to the standardized L 2 distance but also accounts for correlations between the variables. Mahalanobis depth is based on an outlyingness measure (Zuo & Serfling, 2000), viz. Image similarity is the distance between the vectors of two images. affiliations[ ![Heuritech](images/logo heuritech v2. Depending on the data sets you are dealing with there is a high probability that you will need to perform some type of distance computation or similarity computation. Steiger (Vanderbilt University) Outliers, Leverage, and In uence 20 / 45. 2 When two items differ, the distance is positive. mahalanobis distance in c source Search and download mahalanobis distance in c source open source project / source codes from CodeForge. Here, we present to you - Clustering, and it’s variants. G Martos, A Muñoz, J González. The Mahalanobis distance takes into account how spread apart points are in the dataset (i. So we can find that the covariance matrix is also be calculated in the formula. The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. RGB Image clustering using Mahalanobis distance The Mahalanobis distance classification is widely used in clustering. I also previously showed how Mahalanobis distance can be used to compute outliers in multivariate data. This equivalence suggests two different ap-proaches to distance metric learning. In our daily life, we group. 'chebychev' — Chebychev distance, which is the maximum coordinate difference. As now only the mean vector of each class is used, the classification does not take into account how the classes are distributed in the feature space. Note that the matrix L uniquely deﬁnes the matrix M, while the matrix M deﬁnes L up to rotation (which does not affect the computation of distances). Are all the outliers. Spectral Python (SPy) User Guide » Class/Function Glossary¶ File Input/Output¶ Class/Function Description; A classifier using Mahalanobis distance:. For example, in the Euclidean distance metric, the reduced distance is the squared-euclidean distance. We first start with classifying all data points into separate clusters. Written by Peter Rosenmai on 25 Nov 2013. Also, the choice of the distance function is subjective. As we shall see in later examples, it is easy to obtain such plots in R. Euclidean ini biasanya diterapkan pada 2 dimensi dan 3 dimensi. A familiar distance measure which takes into account the. The panel does only appear if there is no distance measure connected (Port 1). Measures of distance between samples: Euclidean We will be talking a lot about distances in this book. 5 let z = generate matrix minkowski distance y1 y2 y3 y4 print z The following output is generated. The text in this article is licensed under the Creative Commons-License Attribution 4. Prasanta Chandra Mahalanobis OBE, FNA, FASc, FRS (29 June 1893 – 28 June 1972) was an Indian Bengali scientist and applied statistician. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. Flexible Data Ingestion. Calculates Mahalanobis depth. Image similarity is the distance between the vectors of two images. Clustering Clustering is the process of examining a collection of "points," and grouping the points into "clusters" according to some distance measure. Euclidean distance is the straight line distance between two points and assumes that the dimensions of the space are orthogonal. Color Supported Generalized-ICP 0 Michael Korn, Martin Holzkothen and Josef Pauli Lehrstuhl Intelligente Systeme, Universitat Duisburg-Essen, 47057 Duisburg, Germany¨. As there are fewer observations than variables, we know the covariance matrix will be singular, so we need to use the singular value decomposition to calculate it. The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. Use Mahalanobis Distance. Podría estar equivocado, a pesar de Esta función calcula el siguiente: D^2 = (x - µ)' Σ^{ -1} (x - µ). Computability, Complexity, & Algorithms Part 1; Topic Modeling Amazon Product Reviews; A Wild Dataset Has Appeared! Now What? Lending Club Data Analysis with Python. 10 new distance nodes have been released that allow the application of various distances measures in combination with the clustering nodes k-Medoids and Hierarchical Clustering, the Similarity Search node, and the Distance Matrix Pair Extractor node. Studied the patterns of the dataset in use and predicted the odds for the correlated parameters using methods like Cook’s distance and Mahalanobis distance. Unlike the variance-based similarity matrices, a PCA performed using Euclidean similarity identiﬁes parameters that are close to each other in a Euclidean distance sense. ZD Javier Gonzalez. A suggestion. for N=100 and fewer than 3 predictors values of Mahalanobis distances greater than 15 are outlying and for N=30 and 2 predictors, values > 11 are outlying. These are the top rated real world Python examples of scipyspatialdistance. I'm sure you know that to multiply 2 matrices, the number of rows in one must equal the number of columns in the other. Where previously I was still using Numpy to compute the inverse of the covariance matrix, I thought it would be fun to do that in TensorFlow itself. affiliations[ ![Heuritech](images/logo heuritech v2. Once a distance measure has been selected, the next step is to use that distance in doing the matching. Mahalanobis distance $= \sqrt{z^T z}$ The second step is a Cholesky decomposition, easily done in MATLAB as L=chol(Sigma,'lower'), or Python as L=numpy. dat y1 y2 y3 y4 skip 0. Python is a great language to solve several problems. To analyze traffic and optimize your experience, we serve cookies on this site. If you are unfamiliar with python, the Python Tutorial is a good start. Mahalanobis Distance¶. For more info on how to get started check Plotly for Python tutorial page here. Intuitively, you could just look at how far v (66, 640, 44) is from the mean of the dataset (68. Latent Dirichlet Allocation (LDA) Latent Dirichlet Allocation (LDA) is a type of probabilistic topic model commonly used in natural language processing to extract topics from large collections of documents in an unsupervised manner. The Mahalanobis distance between 1-D arrays u and v, is defined as. Finding the pixels in the dataset with large Mahalanobis distances was a start, but also selected pixels which were extremely dark — ie, they had a large normalized distance from the mean, but weren’t the bright pixels I was expecting. We first start with classifying all data points into separate clusters. Hi, thank you for your posting! I wonder how do you apply Mahalanobis distanceif you have both continuous and discrete variables. In a regular Euclidean space, variables (e. In this code, I use the SciPy library to take advantage of the built-in function mahalanobis. The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. It might be a good idea to use the Mahalanobis Distance if your data shows high correlation between attributes or if your data is in different units or scales. You can vote up the examples you like or vote down the ones you don't like. But, the data we use for evaluation is deliberately markedly non-multivariate normal since that is what we confront in complex human systems. In the original project, "Health and Local Development: a progress review towards the millennium goals with relation to health in the Brazilian cities which develop. These models are very easy to interpret. between the principal component subspaces while the other is based on the Mahalanobis distance between the datasets. The results are slightly different than the one shown in Section 9. For new samples, the Mahalanobis distance to each of the class centroids is computed and can be used as an additional predictor. Welcome to the 15th part of our Machine Learning with Python tutorial series, where we're currently covering classification with the K Nearest Neighbors algorithm. For a very skewed dataset (such as the one shown on this picture), the Mahalanobis distance (right) may be a better and more intuitive distance metric. Mahalanobis distance is the one also take the covariance of two matrix in consider. Mahalanobis distance is an effective multivariate distance metric that measures the distance between a point and a distribution. They are extracted from open source Python projects. 33 (no units). An example to show covariance estimation with the Mahalanobis distances on Gaussian distributed data. sum((x-y)**2)) a = numpy. Mahalanobis all d> 0 distance between groups weighted by within-group dispersion: metric Distance measures can be categorized as metric, scmimetric. Mahalanobis’ Distance is regard distance between X and Y as same if X and Y have existed over the same ellipse. We proposed a strategy aiming at addressing this issue. Mahalanobis distance. by the MCD estimator. (Some) Gaussian processes, kernels and the kernel trick. Mahalanobis depth is based on an outlyingness measure (Zuo & Serfling, 2000), viz. You can vote up the examples you like or vote down the ones you don't like. Manhattan distance is often used in integrated circuits where wires only run parallel to the X or Y axis. Measures of distance between samples: Euclidean We will be talking a lot about distances in this book. " It sounds much more complicated than it really is. Mahalanobis. 'minkowski' — Minkowski distance with exponent 2. Linear discriminant analysis in R/SAS Comparison with multinomial/logistic regression Iris Data SAS/R Mahalanobis distance The \distance" between classes kand lcan be quanti ed using the Mahalanobis distance: = q ( k l)T 1( k l); Essentially, this is a scale-invariant version of how far apart the means, and which also adjusts for the. Euclidean distance is a measure of the true straight line distance between two points in Euclidean space. 1 thought on “ How To / Python: Calculate Mahalanobis Distance ” Snow July 26, 2017 at 3:11 pm. An alternative interpretation is to investigate any point over 4/n, where n is the number of observations. All data points are classified as a single cluster. Simulation data from two nonlinear dynamic systems: a. mahalanobis¶ scipy. Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. that of Mahalanobis distance which is known to be useful for identifying outliers when data is multivariate normal. You can rate examples to help us improve the quality of examples. • Language used: Python. In cases of uncorrelated variables, the Euclidean Distance is equal to Mahalanobis Distance.


text:
# [OS X TeX] using variables in text via references or labels

Michael Sharpe msharpe at ucsd.edu
Tue Mar 31 17:11:41 CEST 2009

On Mar 30, 2009, at 11:31 AM, Gert van Oss wrote:

> dear all,
>
> I've had some problem making up a clear subject line and stil am in
> doubt whether I've succeded. What I'm trying to achieve is the
> following.
>
> My documents have often various tables and charts embedded via the
>
>   \input{table_file}
>
> command.
>
> While explaining my tables/charts I'm mentioning actual numbers (as
> listed in the tables) in my text. Is it somehow possible to create a
> list of numbers in my latex document and have them called via a
> reference in my text? This would enable me to run a somewhat related
> scenario in my numbers and udpate both my tables with numbers and
> have all numbers changed in the text as well.
>
> I was thinking this should be possible while using \labels, \ref but
> for the moment can't stretch my mind to find a solution.
>

Another option is to use (a modification of) the arrayjob package.
Here's an example.

\usepackage{multido,arrayjobx}%see notes below on arrayjobx
\begin{document}
\newarray\DataA
1&2&3&%
4&5&6&%
7&8&9&%
10&11&12}
\dataheight=3% make rows of 3
% so \DataA(2,3)=6
\begin{tabular}{ccc}
\hline
\textbf{Column 1}&\textbf{Column 2}&\textbf{Column 2}\\
\hline
\let\TableData\empty
%The body of the table has to be constructed in a particular way---see
docs.
\begingroup
\let\DataA\relax
\let\\\relax
\def\rowlength{3}
\multido{\iRow=1+1}{4}{%
\let\RowData\empty
\multido{\iColumn=1+1}{\rowlength}{%
\xdef\RowData{\RowData \DataA(\iRow,\iColumn) \ifx\iColumn
\rowlength \\ \else & \fi}}
\xdef\TableData{\TableData\RowData}}
\endgroup
\TableData
\end{tabular}
The item in row 2, column 3 is \DataA(2,3).

Note on arrayjobx. The package arrayjob conflicts with LaTeX's use of
\array. For my own usage, I edited the file arrayjob.sty to create a
new file arrayjobx.sty, changing the three occurrences of \array to
\Array---lines 108, 148, 164.

Michael
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List Info: http://email.esm.psu.edu/mailman/listinfo/macosx-tex


text:
Getting Data In

## How to set time zone of logs by source?

Path Finder

I’m trying to specify that logs from a certain source coming from a UF are UTC. This should be pretty straightforward, however the following props.conf on the indexers does not work.

[source::c:\\path\\to\\logs\\*]
TZ = Etc/UTC

I’ve tried a .* at the end of the file path and many other variations, nothing works as it should according to the props.conf.spec.

Any ideas?

Thanks

Tags (4)
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text:
# Thread: File dialog box shows all file types rather than selected file types

1. ## File dialog box shows all file types rather than selected file types

Code is:
Code:
```    '   get code for pic
Dim vFile, sPath2Pics, FileChosen
vFile = file
sPath2Pics = CurrentProject.Path
With Application.FileDialog(msoFileDialogFilePicker)
.Filters.Clear
FileChosen = .Show
.Title = "Choose File"
.InitialFileName = sPath2Pics & "\pics\"

.InitialView = msoFileDialogViewList
.Filters.Clear

.ButtonName = "Choose this file"
.AllowMultiSelect = False
.FilterIndex = 1

If FileChosen <> -1 Then
MsgBox "No file chosen !!"
Else
file = .SelectedItems(1)
End If
End With```
The above code shows all files (*.*) in the file dialog box, why is this so?
What does .FilterIndex = 1 do?

2. As it turns out i have solved it by replacing:
to

The All file *.* in the file types at the bowwom don't matter

3. I'm surprised you fixed it like that way, the basic problem is that your initial code shows the dialog before you set it's properties. Set the properties then show the dialog just before you test the return value.

Setting FilterIndex tells the dialog which filter, when you provide multiple filters, is the default. i.e. the one selected before the user drops down the list of filters and selects another.

Ian.

4. Thanks Ian, would you change my code and let me know what you mean please
No matter i did the following:
Code:
```         .Title = "Choose File"
.InitialFileName = sPath2Pics & "\pics\"

.InitialView = msoFileDialogViewList
.Filters.Clear


text:
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text:
# CS 111 Lecture: Sorting¶

## Question: How to sort by elements that are not in the first position?¶

Here is a list of the Space Missions where the second element in the tuple represents the number of days the mission lasted. Some quick terminology:

• Program name refers to 'Apollo' or 'Mercury-Redstone', for example
• Mission number refers to the 11 in 'Apollo 11' or '3' in Gemini 3
• Days refers to the number of days the mission lasted. In truth, many of the missions with one day listed lasted only a matter of minutes but have been rounded to 1 for ease.
In [1]:
missions = [('Apollo 11', 8), ('Mercury-Redstone 3', 1),
('Apollo 13', 5), ('Gemini 3', 1), ('Little Joe 6', 1)]

In [2]:
sorted(missions)

Out[2]:
[('Apollo 11', 8),
('Apollo 13', 5),
('Gemini 3', 1),
('Little Joe 6', 1),
('Mercury-Redstone 3', 1)]

Our Problem: How to sort the missions not by name (default), but by days?

# 1. Sorting with the key parameter¶

Yes! It turns out, the function sorted allows us to perform sorting by using the key parameter, which specifies the element of an item to use for sorting.

In [3]:
help(sorted)

Help on built-in function sorted in module builtins:

sorted(iterable, key=None, reverse=False)
Return a new list containing all items from the iterable in ascending order.

A custom key function can be supplied to customise the sort order, and the
reverse flag can be set to request the result in descending order.

In [4]:
def days(missionTuple):
return missionTuple[1]

In [5]:
sorted(missions, key=days)

Out[5]:
[('Mercury-Redstone 3', 1),
('Gemini 3', 1),
('Little Joe 6', 1),
('Apollo 13', 5),
('Apollo 11', 8)]
In [6]:
# define the function missionLength that will return the length of the
# entire name of the mission (i.e., length of "Apollo 11")
def missionLength(missionTuple):
return len(missionTuple[0])

In [7]:
# use the function missionLength for sorting with key
sorted(missions, key=missionLength)

Out[7]:
[('Gemini 3', 1),
('Apollo 11', 8),
('Apollo 13', 5),
('Little Joe 6', 1),
('Mercury-Redstone 3', 1)]

YOUR TURN: Write functions that will allow you to sort by mission number, name of program (i.e., Apollo, Gemini, ..etc.), and length of mission name:

In [8]:
# define the function missionNumber that will return the mission number from the tuple (mission, days)
# As a reminder, the mission number refers to 11 in 'Apollo 11'
# The return value should be an int
def missionNumber(missionTuple):
return int(missionTuple[0].split()[-1])

In [9]:
# use the function missionNumber for sorting key
sorted(missions, key=missionNumber)

Out[9]:
[('Mercury-Redstone 3', 1),
('Gemini 3', 1),
('Little Joe 6', 1),
('Apollo 11', 8),
('Apollo 13', 5)]
In [10]:
# define the function programName that will return the name of the program from the tuple (mission, days)
# As a reminder, the program name refers to 'Apollo' in 'Apollo 11'
# This is tricky!  You will need to use slicing and the .join() method because a program name could potentially
# be multiple words.
def programName(missionTuple):
return ''.join(missionTuple[0].split()[:-1])

In [11]:
# use the function programName for sorting with key.
sorted(missions, key=programName)

Out[11]:
[('Apollo 11', 8),
('Apollo 13', 5),
('Gemini 3', 1),
('Little Joe 6', 1),
('Mercury-Redstone 3', 1)]

### More complex sorting¶

Things get more complicated in situations where elements in a list to be sorted have the same key, and we want to sort by a second key. For example consider the following mission tuples:

In [12]:
missions2 = [('Big Joe 1', 1), ('Mercury-Atlas 3', 1), ('Apollo 9', 10),
('Gemini 10', 2), ('Gemini 3', 1), ('Gemini 9', 3)]

sorted(missions2) # sorts by mission name by default

Out[12]:
[('Apollo 9', 10),
('Big Joe 1', 1),
('Gemini 10', 2),
('Gemini 3', 1),
('Gemini 9', 3),
('Mercury-Atlas 3', 1)]
In [13]:
sorted(missions2, key=days) # sorts by days

Out[13]:
[('Big Joe 1', 1),
('Mercury-Atlas 3', 1),
('Gemini 3', 1),
('Gemini 10', 2),
('Gemini 9', 3),
('Apollo 9', 10)]

The resulting tuples are indeed sorted by days, but how to explain the order for items with the same days?

Python's sorting functions/methods are stable, which means that items that are equal according to the sorting key have the same relative order as in the original list. (Verify this in the above example.)

How can we sort tuples with the same days alphabetically by the mission number and then the program number?

IMPORTANT: The code below expects you to have defined missionNumber, programName, and days in the exercises above.

In [14]:
# A key function that returns a tuple to specify
# lexicographic ordering by the elements of that tuple.
def daysNumProgram(missionTuple):
return (days(missionTuple), missionNumber(missionTuple), programName(missionTuple))

sorted(missions2, key=daysNumProgram)

Out[14]:
[('Big Joe 1', 1),
('Gemini 3', 1),
('Mercury-Atlas 3', 1),
('Gemini 10', 2),
('Gemini 9', 3),
('Apollo 9', 10)]

YOUR TURN: Below, define numDaysLength so that the it sorts all tuples in missions and missions2 in ascending order first by

• the number of the program, then
• by the number of days the mission lasted,
• then by the length of the program name:

HINT: Make use of the helper functions you created previously.

In [15]:
# Your code here for the definition of numDaysLength
def numDaysLength(missionTuple):
return missionNumber(missionTuple), days(missionTuple), programName(missionTuple)

sorted(missions+missions2, key=numDaysLength)

Out[15]:
[('Big Joe 1', 1),
('Gemini 3', 1),
('Gemini 3', 1),
('Mercury-Atlas 3', 1),
('Mercury-Redstone 3', 1),
('Little Joe 6', 1),
('Gemini 9', 3),
('Apollo 9', 10),
('Gemini 10', 2),
('Apollo 11', 8),
('Apollo 13', 5)]

# 2. Sorting with mutating list methods¶

Python list objects have their methods to sort a list in place (i.e., by mutating the existing list, not returning a new list):

In [16]:
numbers = [35, -2, 17, -9, 0, 12, 19]

In [17]:
numbers.sort()

Notice that nothing was returned.

In [18]:
numbers

Out[18]:
[-9, -2, 0, 12, 17, 19, 35]

Notice that the original list was mutated.

We can reverse the order of items in the list, without sorting:

In [19]:
numbers2 = [35, -2, 17, -9, 0, 12, 19]
numbers2.reverse()

In [20]:
numbers2

Out[20]:
[19, 12, 0, -9, 17, -2, 35]

If we want to reverse the order of a sorted list, we need to sort it firt and then reverse:

In [21]:
numbers2 = [35, -2, 17, -9, 0, 12, 19]
numbers2.sort()
numbers2.reverse()

In [22]:
numbers2

Out[22]:
[35, 19, 17, 12, 0, -2, -9]
In [23]:
help(numbers2.sort)

Help on built-in function sort:

sort(...) method of builtins.list instance
L.sort(key=None, reverse=False) -> None -- stable sort *IN PLACE*

Notice that sort can take the same parameters key and reverse as sorted.

Here is an alternative way of sorting a list in reverse order using sort and passing reverse as an argument.

In [24]:
numbers3 = [35, -2, 17, -9, 0, 12, 19]
numbers3.sort(reverse=True)
numbers3

Out[24]:
[35, 19, 17, 12, 0, -2, -9]


text:
# Introduction

Electronic Health Records (EHR) data is high dimensional, heterogeneous, and sparse, which makes predictive modelling a challenge. In the early days, the machine learning community mainly focused on algorithm development, currently there is a shift to more powerful feature engineering. Deep Learning models are widely used to automatically learn high-level feature representations from the data, and have achieved remarkable results in image processing, speech recognition and computational biology. Recently, interesting results have been shown using EHRs, but more extensive research is needed to assess the power of Deep Learning in this domain.

This vignette describes how you can use the Observational Health Data Sciences and Informatics (OHDSI) PatientLevelPrediction package to build Deep Learning models. This vignette assumes you have read and are comfortable with building patient level prediction models as described in the BuildingPredictiveModels vignette. Furthermore, this vignette assumes you are familiar with Deep Learning methods.

# Background

Deep Learning models are build by stacking an often large number of neural network layers that perform feature engineering steps, e.g embedding, and are collapsed in a final softmax layer (basically a logistic regression layer). These algorithms need a lot of data to converge to a good representation, but currently the sizes of the EHR databases are growing fast which would make Deep Learning an interesting approach to test within OHDSI’s Patient-Level Prediction Framework. The current implementation allows us to perform research at scale on the value and limitations of Deep Learning using EHR data. For relatively small Target and Outcome cohorts, Deep Learning is most probably not the best choice.

Most current Deep Learning research is performed in python and we have developed a pipeline to interact with python. Multiple Deep Learning backends have been developed, e.g. Tensorflow, PyTorch, Keras (recently also available in R) etc. In the package we have implemented interaction with Keras in R and PyTorch in Python but we invite the community to add other backends.

Many network architectures have recently been proposed and we have implemented a number of them, however, this list will grow in the near future. It is important to understand that some of these architectures require a 2D data matrix, i.e. |patient|x|feature|, and others use a 3D data matrix |patient|x|feature|x|time|. The FeatureExtraction Package has been extended to enable the extraction of both data formats as will be described with examples below.

Note that training Deep Learning models is computationally intensive, our implementation therefore supports both GPU and CPU. It will automatically check whether there is GPU or not in your computer. A GPU is highly recommended for Deep Learning!

# Non-Temporal Architectures

We implemented the following non-temporal (2D data matrix) architectures using PyTorch:

1) Logistics regression (LRTorch)
A simple softmax layer with l2 regularization

2) Feed forward network (MLPTorch)
Supports multilayer perceptron (mlp_type = MLP) and
Self-Normalizing Neural Networks (mlp_type = SNN)
Reference: https://arxiv.org/abs/1706.02515

For the above two methods, we implemented support for a stacked autoencoder and a variational autoencoder to reduce the feature dimension as a first step. These autoencoders learn efficient data encodings in an unsupervised manner by stacking multiple layers in a neural network. Compared to the standard implementations of LR and MLP these implementations can use the GPU power to speed up the gradient descent approach in the back propagation to optimize the weights of the classifier.

Table 1: Non-Temporal Deep Learning Models Hyper-Parameters

Name Description Hyper-parameters
LRTorch Logistic Regression Model w_decay (l2 regularization), epochs (number of epochs), class_weight (0 = inverse ratio between number of positive and negative examples, -1 = focal loss (https://arxiv.org/abs/1708.02002), or other), autoencoder (apply stacked autoencoder?, vae (apply variational autoencoder)
MLPTorch Multi-Layer Perceptron Model mlp_type (MLP = default, SNN = self-normalizing neural network), size (number of hidden nodes), w_decay (l2 regularization), epochs (number of epochs), class_weight(0 = inverse ratio between number of positive and negative examples, -1 = focal loss, or other), autoencoder (apply stacked autoencoder), vae (apply variational autoencoder?)

##Example The approach for logistic regression (LRTorch) and the Multi-Layer Perceptron (MLPTorch) is identical. Here we will take LRTorch as an example.

You need to generate a population and plpData object as described in more detail in BuildingPredictiveModels vignette.

Alternatively, you can make use of the data simulator. The following code snippet creates a population of 12000 patients.

set.seed(1234)
data(plpDataSimulationProfile)
sampleSize <- 12000
plpData <- simulatePlpData(
plpDataSimulationProfile,
n = sampleSize
)

population <- createStudyPopulation(
plpData,
outcomeId = 2,
binary = TRUE,
firstExposureOnly = FALSE,
washoutPeriod = 0,
removeSubjectsWithPriorOutcome = FALSE,
priorOutcomeLookback = 99999,
requireTimeAtRisk = FALSE,
minTimeAtRisk = 0,
riskWindowStart = 0,
riskWindowEnd = 365,
verbosity = "INFO"
)

As an example we will build a LRTorch model. We could specify the stacked autoencoder or the variational autoencoder to be used for reducing the feature dimension as an initial layer, but for this example we do not.

autoencoder <- FALSE
vae <- FALSE

We added a class_weight for imbalanced data, the default value 0 is the inverse ratio between negatives and positives,-1 applies focal loss.

class_weight <- 0
# Specify the settings for Logistics regression model using Torch in Python
model <- setLRTorch(autoencoder=autoencoder, vae=vae,  class_weight=class_weight)

No we define our modelling parameters.

testFraction <- 0.2
testSplit <- 'person'
nfold <- 3
splitSeed <- 1000

And we train and internally validate the model.

results <- PatientLevelPrediction::runPlp(population = population,
plpData = plpData,
modelSettings = model,
testSplit=testSplit,
testFraction=testFraction,
nfold=nfold,
splitSeed=splitSeed)

# Temporal Architectures

Several architectures are implemented that can handle temporal data in PyTorch and R Keras.

## PyTorch CNN

We implemented the following convolutional models described in https://github.com/clinicalml/deepDiagnosis in CNNTorch:

1. Temporal Convolutional neural network over a backward window (type = cnn)
2. Convolutional neural network over input and time dimension (type = mix)
3. Multi-resolution temporal convolutional neural network (type = multi)

Furthermore, we added the following achitectures:

1. CNN with filters with three different parallel kernel sizes (3,4,5) and a fully connected layers (type = mlf)
2. LSTM network over the backward window (type = lstm)
3. Residual Learning Network as described in: https://arxiv.org/abs/1512.03385 (type = resnet)
This a very big network, see the paper for the topology.
parameter description
nbfilters The number of convolution filters
epochs The number of epochs
seed Random seed
class_weight The class weight used for imbalanced data
(0: Inverse ratio between positives and negatives, -1: Focal loss, or number)

## PyTorch RNN

The following recurrent neural network models are implemented in RNNTorch:

1. RNN with one LSTM layer fed into one fully connected layer (type = RNN)
2. RNN with one bidirectional LSTM layer fed into one fully connected layer (type = BiRNN)
This network looks the same as above but then as a bi-directional version
3. One Gated Recurrent Unit layer fed into one fully connected layers (type = GRU)
This network looks the same as above but then implemented as GRU

The following hyper-parameters can be set for these PyTorch models:

parameter description
hidden_size The number of features in hidden state
epochs The number of epochs
seed Random seed
class_weight The class weight used for imbalanced data
(0: Inverse ratio between positives and negatives, -1: Focal loss, or number)

## R Keras CNN

The following temporal architectures as described in https://arxiv.org/pdf/1608.00647.pdf were implemented using R Keras:

1. Multi-resolution CovNN model (CovNN.R)
2. Convolution across data and time according(CovNN2.R)

Furthermore, a custom build RNN is added that uses a variational autoencoder.

1. Clinically Informing application based on Recurrent Neural Network (CIReNN.R)

Table 2: Temporal Deep Learning Models

Model Hyper-parameters
CovNN batchSize (The number of samples to used in each batch during model training), outcomeWeight (The weight assigned to the outcome), lr (The learning rate), decay (The decay of the learning rate), dropout ([currently not used] the dropout rate for regularization), epochs (The number of times data is used to train the model, e.g., epoches=1 means data only used once to train), filters (The number of columns output by each convolution), kernelSize (The number of time dimensions used for each convolution), loss (The loss function implemented), seed (The random seed)
CovNN2 batchSize (The number of samples to used in each batch during model training), outcomeWeight (The weight assigned to the outcome), lr (The learning rate), decay (The decay of the learning rate), dropout ([currently not used] the dropout rate for regularization), epochs (The number of times data is used to train the model, e.g., epoches=1 means data only used once to train), filters (The number of columns output by each convolution), kernelSize (The number of time dimensions used for each convolution), loss (The loss function implemented), seed (The random seed)
CIReNN units (The number of units of RNN layer - as a list of vectors), recurrentDropout (The reccurrent dropout rate), layerDropout (The layer dropout rate), lr (Learning rate), decay (Learning rate decay over each update), outcomeWeight (The weight of the outcome class in the loss function), batchSize (The number of data points to use per training batch), epochs (Number of times to iterate over data set), earlyStoppingMinDelta (Minimum change in the monitored quantity to qualify as an improvement for early stopping, i.e. an absolute change of less than min_delta in loss of validation data, will count as no improvement), earlyStoppingPatience (Number of epochs with no improvement after which training will be stopped), seed (Random seed used by Deep Learning model)

## Example

We will now show how to use the temporal models by using CNNTorch as an example.

You need to generate a population and plpData object as described in more detail in BuildingPredictiveModels vignette.

Note that for these algorithms you need to extracted temporal data as described in the [FeatureExtraction vignette] (https://github.com/OHDSI/FeatureExtraction/blob/master/inst/doc/UsingFeatureExtraction.pdf) as follows:

settings <- createTemporalCovariateSettings(useConditionEraStart = FALSE,
useConditionEraOverlap = FALSE,
useConditionOccurrence = FALSE,
useConditionEraGroupStart = FALSE,
useConditionEraGroupOverlap = FALSE,
useDrugExposure = FALSE,
useDrugEraStart = FALSE,
useDrugEraOverlap = FALSE,
useMeasurement = FALSE,
useMeasurementValue = TRUE,
useMeasurementRangeGroup = FALSE,
useProcedureOccurrence = FALSE,
useDeviceExposure = FALSE,
useObservation = FALSE,
excludedCovariateConceptIds = c(316866),
temporalStartDays = seq(from = -365,
to = -1, by = 12),
temporalEndDays = c(seq(from = -353,
to = 0, by = 12), 0))

plpData <- getPlpData(connectionDetails = connectionDetails,
cdmDatabaseSchema = cdmDatabaseSchema,
cohortDatabaseSchema = "results",
cohortTable = "cohort",
cohortId = 11,
covariateSettings = settings,
outcomeDatabaseSchema = resultsDatabaseSchema,
outcomeTable = "cohort",
outcomeIds = 25,
cdmVersion = 5)

Each CNN/RNN has several hyper-parameters that can be set as shown in the Tables above, but for this example we take the defaults.

# specify the the CNN
model <- setCNNTorch(cnn_type='CNN')

Run the model training, for example with a testFraction = 0.2 and a split by person:

results <- PatientLevelPrediction::runPlp(population, plpData, model,
testSplit='person',
testFraction=0.2,
nfold=3,
splitSeed=1000)

# Apply the trained Deep Learning model

Applying a Deep Learning is identical to the other models in the package:

# load the trained model

# load the new plpData (should have the same temporal features!) and create the population

populationSettings <- plpModel$populationSettings populationSettings$plpData <- plpData
population <- do.call(createStudyPopulation, populationSettings)

# apply the trained model on the new data
validationResults <- applyModel(population, plpData, plpModel)

It is possible to add new architectures in our framework using PyTorch or R Keras. We are happy to help you with this, please post your questions on the issue tracker of the package.

# Acknowledgments

Considerable work has been dedicated to provide the PatientLevelPrediction package.

citation("PatientLevelPrediction")
##
## To cite PatientLevelPrediction in publications use:
##
## Reps JM, Schuemie MJ, Suchard MA, Ryan PB, Rijnbeek P (2018). "Design
## and implementation of a standardized framework to generate and evaluate
## patient-level prediction models using observational healthcare data."
## _Journal of the American Medical Informatics Association_, *25*(8),
## 969-975. <URL: https://doi.org/10.1093/jamia/ocy032>.
##
## A BibTeX entry for LaTeX users is
##
##   @Article{,
##     author = {J. M. Reps and M. J. Schuemie and M. A. Suchard and P. B. Ryan and P. Rijnbeek},
##     title = {Design and implementation of a standardized framework to generate and evaluate patient-level prediction models using observational healthcare data},
##     journal = {Journal of the American Medical Informatics Association},
##     volume = {25},
##     number = {8},
##     pages = {969-975},
##     year = {2018},
##     url = {https://doi.org/10.1093/jamia/ocy032},
##   }

Please reference this paper if you use the PLP Package in your work:

Reps JM, Schuemie MJ, Suchard MA, Ryan PB, Rijnbeek PR. Design and implementation of a standardized framework to generate and evaluate patient-level prediction models using observational healthcare data. J Am Med Inform Assoc. 2018;25(8):969-975.