In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis Ziqi Wang a, Marco Broccardo b a Earthquake Engineering Research and Test Center, Guangzhou University, China b Swiss Seismological Service, SED, ETH Z urich, SwitzerlandAbstract This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches for reliability (rare event probability) analysis of expensive black-box solvers. A naive iteration of these algorithms with respect to different CDF/CCDF threshold values would yield a discretized CDF/CCDF. However, this approach inevitably leads to a trade off between accuracy and computational efficiency since both depend (in opposite way) on the selected discretization. In this study, a specialized error measure and a learning function are developed such that the resulting AL-GP method is able to efficiently estimate the CDF/CCDF for a specified range of interest without an explicit dependency on discretization. Particularly, the proposed AL-GP method is able to simultaneously provide accurate CDF and CCDF estimation in their median-low probability regions. Three numerical examples are introduced to test and verify the proposed method. Introduction In a broad sense, uncertainty quantification (UQ) refers to the theory and practice to obtain quantitative understanding on the influences of uncertainties present within computational or real physical models. There are intrinsic connections between various branches of UQ, and attempts are made to develop unified UQ frameworks [4][5]. This study focuses on a central problem in forward UQ problems, the estimation of distribution function, i.e. cumulative and complementary cumulative distribution function (CDF/CCDF).

We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show that it achieves the same accuracy of exact kernel k-means with only a fraction of computations. Indeed, we prove under basic assumptions that sampling $\sqrt{n}$ Nystr\"om landmarks allows to greatly reduce computational costs without incurring in any loss of accuracy. To the best of our knowledge this is the first result of this kind for unsupervised learning.

Image modality recognition is essential for efficient imaging workflows in current clinical environments, where multiple imaging modalities are used to better comprehend complex diseases. Emerging biomarkers from novel, rare modalities are being developed to aid in such understanding, however the availability of these images is often limited. This scenario raises the necessity of recognising new imaging modalities without them being collected and annotated in large amounts. In this work, we present a few-shot learning model for limited training examples based on Deep Triplet Networks. We show that the proposed model is more accurate in distinguishing different modalities than a traditional Convolutional Neural Network classifier when limited samples are available. Furthermore, we evaluate the performance of both classifiers when presented with noisy samples and provide an initial inspection of how the proposed model can incorporate measures of uncertainty to be more robust against out-of-sample examples.

Accurate m odel selection is a fundamental requirement for statistical analysis (1 - 5) . In many real - world applications of graphical modelling, correct model structure ident ifica tion is the ultimate objective. S tandard model validation procedures such as information theoretic scores and cross validation have demonstr ated poor performance when . Specialised methods such as EBIC, StARS and RIC have been developed for the explicit purpose of high - dimensional Gaussian graphical model selection. We present a novel model score criterion, Graphical Neighbour Information. This method demonstrates oracle performance in high - dimensional model selection, outperforming the current state - of - the - a rt in our simulations. The Graphical Neighbour Information criterion has the additional advantage of efficient, closed - form computability, sparing the costly inference of multiple models on data subsamples. We provide a theoretic analysis of the method and benchmark simulations versus the current state of the art .

We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error probability. With Sanov's theorem, we derive a sufficient condition for one-sample tests to achieve the optimal error exponent in the universal setting, i.e., for any distribution defining the alternative hypothesis. We then show that two classes of Maximum Mean Discrepancy (MMD) based tests attain the optimal type-II error exponent on $\mathbb R^d$, while the quadratic-time Kernel Stein Discrepancy (KSD) based tests achieve this optimality with an asymptotic level constraint. For general two-sample testing, however, Sanov's theorem is insufficient to obtain a similar sufficient condition. We proceed to establish an extended version of Sanov's theorem and derive an exact error exponent for the quadratic-time MMD based two-sample tests. The obtained error exponent is further shown to be optimal among all two-sample tests satisfying a given level constraint. Our results not only solve a long-standing open problem in information theory and statistics, but also provide an achievability result for optimal nonparametric one- and two-sample testing. Application to off-line change detection and related issues are also discussed.

We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $. This model is motivated by applications such as channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on by a given channel/filter, and phase information is difficult or impossible to acquire. We show that when $\mathbf a$ is random and the number of observations $m$ is sufficiently large, with high probability $\mathbf x$ can be efficiently recovered up to a global phase shift using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator. We overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis for alternating minimization methods.

This article describes my machine learning project on credit card fraud. If you are interested in the code, you can find my notebook here. Ever since starting my journey into data science, I have been thinking about ways to use data science for good while generating value at the same time. Thus, when I came across this data set on Kaggle dealing with credit card fraud detection, I was immediately hooked. The data set has 31 features, 28 of which have been anonymized and are labeled V1 through V28.

I've implemented SVRG (Stochastic Variance Reduction Gradient Descent) optimizer for Keras. The goal is to make this optimizer available in Keras as well, which may be beneficial in the case of RL as some papers claimed it is advantageous over Adam.

K-Means clustering method considers two assumptions regarding the clusters -- first that the clusters are spherical and second that the clusters are of similar size. Spherical assumption helps in separating the clusters when the algorithm works on the data and forms clusters. If this assumption is violated, the clusters formed may not be what one expects. On the other hand, assumption over the size of clusters helps in deciding the boundaries of the cluster. Certain resemblance measures (e.g., Euclidean distance)assume that the variables are uncorrelated within clusters.