As the manufacturing industry is moving away from the traditional long term service contract to an'Analytics-as-a-Service' model, big data applications are increasingly being used to collect data from manufacturing operations. Using big data, you can accurately predict failure in operations well ahead of time, increasing the service revenue and reducing the cost of service. In addition, you can predict the health of your equipment in real time, and release equipment for maintenance only when necessary. Through the use of neural networks, support vector machines, and decision trees, you can identify complex interdependencies within operational parameters and detect anomalies that lead to equipment failures.

The metamorphic malware variants with the same malicious behavior (family), can obfuscate themselves to look different from each other. This variation in structure leads to a huge signature database for traditional signature matching techniques to detect them. In order to effective and efficient detection of malware in large amounts of executables, we need to partition these files into groups which can identify their respective families. In addition, the grouping criteria should be chosen such a way that, it can also be applied to unknown files encounter on computers for classification. This paper discusses the study of malware and benign executables in groups to detect unknown malware with high accuracy. We studied sizes of malware generated by three popular second generation malware (metamorphic malware) creator kits viz. G2, PS-MPC and NGVCK, and observed that the size variation in any two generated malware from same kit is not much. Hence, we grouped the executables on the basis of malware sizes by using Optimal k-Means Clustering algorithm and used these obtained groups to select promising features for training (Random forest, J48, LMT, FT and NBT) classifiers to detect variants of malware or unknown malware. We find that detection of malware on the basis of their respected file sizes gives accuracy up to 99.11% from the classifiers.

Bayesian hierarchical models are increasing popular in economics. When using hierarchical models, it is useful not only to calculate posterior expectations, but also to measure the robustness of these expectations to reasonable alternative prior choices. We use variational Bayes and linear response methods to provide fast, accurate posterior means and robustness measures with an application to measuring the effectiveness of microcredit in the developing world.

Deep Reinforcement Learning (DRL) is a trending field of research, showing great promise in many challenging problems such as playing Atari, solving Go and controlling robots. While DRL agents perform well in practice we are still missing the tools to analayze their performance and visualize the temporal abstractions that they learn. In this paper, we present a novel method that automatically discovers an internal Semi Markov Decision Process (SMDP) model in the Deep Q Network's (DQN) learned representation. We suggest a novel visualization method that represents the SMDP model by a directed graph and visualize it above a t-SNE map. We show how can we interpret the agent's policy and give evidence for the hierarchical state aggregation that DQNs are learning automatically. Our algorithm is fully automatic, does not require any domain specific knowledge and is evaluated by a novel likelihood based evaluation criteria.

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like this often come from human judgments. To account for errors and variation in judgments, we consider the noisy situation in which the given constraints are independently corrupted by reversing the correct constraint with some probability. This paper makes several new contributions to this problem. First, we derive prediction error bounds for ordinal embedding with noise by exploiting the fact that the rank of a distance matrix of points in $\mathbb{R}^d$ is at most $d+2$. These bounds characterize how well a learned embedding predicts new comparative judgments. Second, we investigate the special case of a known noise model and study the Maximum Likelihood estimator. Third, knowledge of the noise model enables us to relate prediction errors to embedding accuracy. This relationship is highly non-trivial since we show that the linear map corresponding to distance comparisons is non-invertible, but there exists a nonlinear map that is invertible. Fourth, two new algorithms for ordinal embedding are proposed and evaluated in experiments.

Many predictive tasks, such as diagnosing a patient based on their medical chart, are ultimately defined by the decisions of human experts. Unfortunately, encoding experts' knowledge is often time consuming and expensive. We propose a simple way to use fuzzy and informal knowledge from experts to guide discovery of interpretable latent topics in text. The underlying intuition of our approach is that latent factors should be informative about both correlations in the data and a set of relevance variables specified by an expert. Mathematically, this approach is a combination of the information bottleneck and Total Correlation Explanation (CorEx). We give a preliminary evaluation of Anchored CorEx, showing that it produces more coherent and interpretable topics on two distinct corpora.

It is known that for a certain class of single index models (SIMs) $Y = f(\boldsymbol{X}_{p \times 1}^\intercal\boldsymbol{\beta}_0, \varepsilon)$, support recovery is impossible when $\boldsymbol{X} \sim \mathcal{N}(0, \mathbb{I}_{p \times p})$ and a model complexity adjusted sample size is below a critical threshold. Recently, optimal algorithms based on Sliced Inverse Regression (SIR) were suggested. These algorithms work provably under the assumption that the design $\boldsymbol{X}$ comes from an i.i.d. Gaussian distribution. In the present paper we analyze algorithms based on covariance screening and least squares with $L_1$ penalization (i.e. LASSO) and demonstrate that they can also enjoy optimal (up to a scalar) rescaled sample size in terms of support recovery, albeit under slightly different assumptions on $f$ and $\varepsilon$ compared to the SIR based algorithms. Furthermore, we show more generally, that LASSO succeeds in recovering the signed support of $\boldsymbol{\beta}_0$ if $\boldsymbol{X} \sim \mathcal{N}(0, \boldsymbol{\Sigma})$, and the covariance $\boldsymbol{\Sigma}$ satisfies the irrepresentable condition. Our work extends existing results on the support recovery of LASSO for the linear model, to a more general class of SIMs.

In this paper we study the support recovery problem for single index models $Y=f(\boldsymbol{X}^{\intercal} \boldsymbol{\beta},\varepsilon)$, where $f$ is an unknown link function, $\boldsymbol{X}\sim N_p(0,\mathbb{I}_{p})$ and $\boldsymbol{\beta}$ is an $s$-sparse unit vector such that $\boldsymbol{\beta}_{i}\in \{\pm\frac{1}{\sqrt{s}},0\}$. In particular, we look into the performance of two computationally inexpensive algorithms: (a) the diagonal thresholding sliced inverse regression (DT-SIR) introduced by Lin et al. (2015); and (b) a semi-definite programming (SDP) approach inspired by Amini & Wainwright (2008). When $s=O(p^{1-\delta})$ for some $\delta>0$, we demonstrate that both procedures can succeed in recovering the support of $\boldsymbol{\beta}$ as long as the rescaled sample size $\kappa=\frac{n}{s\log(p-s)}$ is larger than a certain critical threshold. On the other hand, when $\kappa$ is smaller than a critical value, any algorithm fails to recover the support with probability at least $\frac{1}{2}$ asymptotically. In other words, we demonstrate that both DT-SIR and the SDP approach are optimal (up to a scalar) for recovering the support of $\boldsymbol{\beta}$ in terms of sample size. We provide extensive simulations, as well as a real dataset application to help verify our theoretical observations.

We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the fitted estimating equations to a sparse direction obtained by solving a large-scale linear program. Our main theoretical contribution is to establish a unified Z-estimation theory of confidence regions for high dimensional problems. Different from existing methods, all of which require the specification of the likelihood or pseudo-likelihood, our framework is likelihood-free. As a result, our approach provides valid inference for a broad class of high dimensional constrained estimating equation problems, which are not covered by existing methods. Such examples include, noisy compressed sensing, instrumental variable regression, undirected graphical models, discriminant analysis and vector autoregressive models. We present detailed theoretical results for all these examples. Finally, we conduct thorough numerical simulations, and a real dataset analysis to back up the developed theoretical results.

The analysis of large and possibly high-dimensional datasets is becoming ubiquitous in the sciences. The long-term objective is to gain insight into the structure of measurement or simulation data, for a better understanding of the underlying physical phenomena at work. Clustering is one of the simplest ways of gaining such insight, by finding a suitable decomposition of the data into clusters such that data points within a same cluster share common (and, if possible, exclusive) properties. In this work, we are interested in the mode seeking approach to clustering. This approach assumes the data points to be drawn from some unknown probability distribution and defines the clusters as the basins of attraction of the maxima of the density, requiring a preliminary density estimation phase [7, 5, 10, 11, 13, 15]. The theoretical analysis of this clustering framework has drawn increasing attention recently, see 1 [6, 3, 9, 8, 2]. However, this (hard) clustering method provides a fairly limited knowledge on the structure of the data: while the partition into clusters is well understood, the interplay between clusters (respective locations, proximity relations, interactions) remains unknown. Identifying interfaces between clusters is the first step towards a higher-level understanding of the data, and it already plays a prominent role in some applications such as the study of the conformations space of a protein, where a fundamental question beyond the detection of metastable states is to understand when and how the protein can switch from one metastable state to another [12]. Hard clustering can be used in this context, for instance by defining the border between two clusters as the set of data points whose neighborhood (in the ambient space or in some neighborhood graph) intersects the two clusters, however this kind of information is by nature unstable with respect to perturbations of the data.