The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One natural question that arises is that, as in the inductive setting, if features are provided as input as well, can we hope to do better? Answering this in the affirmative, the main goal of this paper is to study the robust PCA problem while incorporating feature information. In contrast to previous works in which recovery guarantees are based on the convex relaxation of the problem, we propose a simple iterative algorithm based on hard-thresholding of appropriate residuals. Under weaker assumptions than previous works, we prove the global convergence of our iterative procedure; moreover, it admits a much faster convergence rate and lesser computational complexity per iteration. In practice, through systematic synthetic and real data simulations, we confirm our theoretical findings regarding improvements obtained by using feature information.

We present a novel subset scan method to detect if a probabilistic binary classifier has statistically significant bias -- over or under predicting the risk -- for some subgroup, and identify the characteristics of this subgroup. This form of model checking and goodness-of-fit test provides a way to interpretably detect the presence of classifier bias or regions of poor classifier fit. This allows consideration of not just subgroups of a priori interest or small dimensions, but the space of all possible subgroups of features. To address the difficulty of considering these exponentially many possible subgroups, we use subset scan and parametric bootstrap-based methods. Extending this method, we can penalize the complexity of the detected subgroup and also identify subgroups with high classification errors. We demonstrate these methods and find interesting results on the COMPAS crime recidivism and credit delinquency data.

As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that such subgraphs can be recovered from the solution of a particular semidefinite relaxation with high probability if the input graph is sampled from a distribution of clusterable graphs. Specifically, the semidefinite relaxation is exact if the graph consists of k large disjoint subgraphs, corresponding to clusters, with weight concentrated within these subgraphs, plus a moderate number of outliers. Further, we establish that if noise is weakly obscuring these clusters, i.e, the between-cluster edges are assigned very small weights, then we can recover significantly smaller clusters. For example, we show that in approximately sparse graphs, where the between-cluster weights tend to zero as the size n of the graph tends to infinity, we can recover clusters of size polylogarithmic in n. Empirical evidence from numerical simulations is also provided to support these theoretical phase transitions to perfect recovery of the cluster structure.

The optimization of composition and processing to obtain materials that exhibit desirable characteristics has historically relied on a combination of scientist intuition, trial and error, and luck. We propose a methodology that can accelerate this process by fitting data-driven models to experimental data as it is collected to suggest which experiment should be performed next. This methodology can guide the scientist to test the most promising candidates earlier, and can supplement scientific intuition and knowledge with data-driven insights. A key strength of the proposed framework is that it scales to high-dimensional parameter spaces, as are typical in materials discovery applications. Importantly, the data-driven models incorporate uncertainty analysis, so that new experiments are proposed based on a combination of exploring high-uncertainty candidates and exploiting high-performing regions of parameter space. Over four materials science test cases, our methodology led to the optimal candidate being found with three times fewer required measurements than random guessing on average.

A causal falling rule list (CFRL) is a sequence of if-then rules that specifies heterogeneous treatment effects, where (i) the order of rules determines the treatment effect subgroup a subject belongs to, and (ii) the treatment effect decreases monotonically down the list. A given CFRL parameterizes a hierarchical bayesian regression model in which the treatment effects are incorporated as parameters, and assumed constant within model-specific subgroups. We formulate the search for the CFRL best supported by the data as a Bayesian model selection problem, where we perform a search over the space of CFRL models, and approximate the evidence for a given CFRL model using standard variational techniques. We apply CFRL to a census wage dataset to identify subgroups of differing wage inequalities between men and women.

New tutorial on unsupervised pre-training with stacked denoising auto-encoders. An IJulia Notebook demo of using pre-trained CNN on imagenet to do image classification.

Linear Regression is still the most prominently used statistical technique in data science industry and in academia to explain relationships between features. A total of 1,355 people registered for this skill test. It was specially designed for you to test your knowledge on linear regression techniques. If you are one of those who missed out on this skill test, here are the questions and solutions. You missed on the real time test, but can read this article to find out how many could have answered correctly.

Providing a broad but in-depth introduction to neural network and machine learning in a statistical framework, this book provides a single, comprehensive resource for study and further research. All the major popular neural network models and statistical learning approaches are covered with examples and exercises in every chapter to develop a practical working understanding of the content. Each of the twenty-five chapters includes state-of-the-art descriptions and important research results on the respective topics. The broad coverage includes the multilayer perceptron, the Hopfield network, associative memory models, clustering models and algorithms, the radial basis function network, recurrent neural networks, principal component analysis, nonnegative matrix factorization, independent component analysis, discriminant analysis, support vector machines, kernel methods, reinforcement learning, probabilistic and Bayesian networks, data fusion and ensemble learning, fuzzy sets and logic, neurofuzzy models, hardware implementations, and some machine learning topics. Applications to biometric/bioinformatics and data mining are also included.

Contributed by Jennifer L. Eberhardt, March 26, 2017 (sent for review February 14, 2017; reviewed by James Pennebaker and Tom Tyler) Police officers speak significantly less respectfully to black than to white community members in everyday traffic stops, even after controlling for officer race, infraction severity, stop location, and stop outcome. This paper presents a systematic analysis of officer body-worn camera footage, using computational linguistic techniques to automatically measure the respect level that officers display to community members. This work demonstrates that body camera footage can be used as a rich source of data rather than merely archival evidence, and paves the way for developing powerful language-based tools for studying and potentially improving police–community relations. Using footage from body-worn cameras, we analyze the respectfulness of police officer language toward white and black community members during routine traffic stops. We develop computational linguistic methods that extract levels of respect automatically from transcripts, informed by a thin-slicing study of participant ratings of officer utterances. We find that officers speak with consistently less respect toward black versus white community members, even after controlling for the race of the officer, the severity of the infraction, the location of the stop, and the outcome of the stop. Such disparities in common, everyday interactions between police and the communities they serve have important implications for procedural justice and the building of police–community trust. Over the last several years, our nation has been rocked by an onslaught of incidents captured on video involving police officers' use of force with black suspects.

We propose a number of new algorithms for learning deep energy models from data motivated by a recent Stein variational gradient descent (SVGD) algorithm, including a Stein contrastive divergence (SteinCD) that integrates CD with SVGD based on their theoretical connections, and a SteinGAN that trains an auxiliary generator to generate the negative samples in maximum likelihood estimation (MLE). We demonstrate that our SteinCD trains models with good generalization (high test likelihood), while Stein-GAN can generate realistic looking images competitive with GAN-style methods. We show that by combing SteinCD and SteinGAN, it is possible to inherent the advantage of both approaches.