Approximate inference algorithm is one of the fundamental research fields in machine learning. The two dominant theoretical inference frameworks in machine learning are variational inference (VI) and Markov chain Monte Carlo (MCMC). However, because of the fundamental limitation in the theory, it is very challenging to improve existing VI and MCMC methods on both the computational scalability and statistical efficiency. To overcome this obstacle, we propose a new theoretical inference framework called ergodic Inference based on the fundamental property of ergodic transformations. The key contribution of this work is to establish the theoretical foundation of ergodic inference for the development of practical algorithms in future work.

Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery technique to correctly identify the support with increasing signal to noise ratio (SNR) is an increasingly popular criterion to qualify the high SNR optimality of support recovery techniques. The HSC results available in literature for support recovery techniques applicable to underdetermined linear regression models like least absolute shrinkage and selection operator (LASSO), orthogonal matching pursuit (OMP) etc. assume \textit{a priori} knowledge of noise variance or signal sparsity. However, both these parameters are unavailable in most practical applications. Further, it is extremely difficult to estimate noise variance or signal sparsity in underdetermined regression models. This limits the utility of existing HSC results. In this article, we propose two techniques, \textit{viz.}, residual ratio minimization (RRM) and residual ratio thresholding with adaptation (RRTA) to operate OMP algorithm without the \textit{a priroi} knowledge of noise variance and signal sparsity and establish their HSC analytically and numerically. To the best of our knowledge, these are the first and only noise statistics oblivious algorithms to report HSC in underdetermined regression models.

Humanoid robots have apparently similar body structure like human beings. Due to their technical design, they are sharing the same workspace with humans. They are placed to clean things, to assist old age people, to entertain us and most importantly to serve us. To be acceptable in the household, they must have higher level of intelligence than industrial robots and they must be social and capable of interacting people around it, who are not supposed to be robot specialist. All these come under the field of human robot interaction (HRI). There are various modes like speech, gesture, behavior etc. through which human can interact with robots. To solve all these challenges, a multimodel technique has been introduced where gesture as well as speech is used as a mode of interaction.

Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis, where the classification models to be learned need to fulfil restrictions of monotonicity (i.e. the target class label should not decrease when input attributes values increase). For instance, it is rational to assume that a higher debt ratio of a company should never result in a lower level of bankruptcy risk. Consequently, there is a growing interest from the data mining research community concerning monotonic predictive models. This paper aims to present an overview about the literature in the field, analyzing existing techniques and proposing a taxonomy of the algorithms based on the type of model generated. For each method, we review the quality metrics considered in the evaluation and the different data sets and monotonic problems used in the analysis. In this way, this paper serves as an overview of the research about monotonic classification in specialized literature and can be used as a functional guide of the field.

Previous works observed the spectrum of the Hessian of the training loss of deep neural networks. However, the networks considered were of minuscule size. We apply state-of-the-art tools in modern high-dimensional numerical linear algebra to approximate the spectrum of the Hessian of deep nets with tens of millions of parameters. Our results corroborate previous findings, based on small-scale networks, that the Hessian exhibits 'spiked' behavior, with several outliers isolated from a continuous bulk. However we find that the bulk does not follow a simple Marchenko-Pastur distribution, as previously suggested, but rather a heavier-tailed distribution. Finally, we document the dynamics of the outliers and the bulk with varying sample size.

Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine hyper-parameter tuning in order to achieve its best performance. This has led to the development of adaptive methods, that claim automatic hyper-parameter tuning. Recently, researchers have studied both algorithmic classes via thoughtful toy problems: e.g., for over-parameterized linear regression, [1] shows that, while SGD always converges to the minimum-norm solution (similar to the case of the maximum margin solution in SVMs that guarantees good prediction error), adaptive methods show no such inclination, leading to worse generalization capabilities. Our aim is to study this conjecture further. We empirically show that the minimum norm solution is not necessarily the proper gauge of good generalization in simplified scenaria, and different models found by adaptive methods could outperform plain gradient methods. In practical DNN settings, we observe that adaptive methods often perform at least as well as SGD, without necessarily reducing the amount of tuning required.

We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with $k$ blocks of equal size. More precisely, we consider a random $d$-uniform hypergraph $H$ with $n$ vertices partitioned into $k$ clusters of size $s = n / k$. Hyperedges $e$ are added independently with probability $p$ if $e$ is contained within a single cluster and $q$ otherwise, where $0 \leq q < p \leq 1$. We present a spectral algorithm which recovers the clusters exactly with high probability, given mild conditions on $n, k, p, q$, and $d$. Our algorithm is based on the adjacency matrix of $H$, which we define to be the symmetric $n \times n$ matrix whose $(u, v)$-th entry is the number of hyperedges containing both $u$ and $v$. To the best of our knowledge, our algorithm is the first to guarantee exact recovery when the number of clusters $k=\Theta(\sqrt{n})$.

This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between original and knockoff features. By building upon the existing model-X framework, we thus obtain a flexible and model-free statistical tool to perform controlled variable selection. Extensive numerical experiments and quantitative tests confirm the generality, effectiveness, and power of our deep knockoff machines. Finally, we apply this new method to a real study of mutations linked to changes in drug resistance in the human immunodeficiency virus.

We cast the problem of combinatorial auction design in a Bayesian framework in order to incorporate prior information into the auction process and minimize the number of rounds to convergence. We first develop a generative model of agent valuations and market prices such that clearing prices become maximum a posteriori estimates given observed agent valuations. This generative model then forms the basis of an auction process which alternates between refining estimates of agent valuations and computing candidate clearing prices. We provide an implementation of the auction using assumed density filtering to estimate valuations and expectation maximization to compute prices. An empirical evaluation over a range of valuation domains demonstrates that our Bayesian auction mechanism is highly competitive against the combinatorial clock auction in terms of rounds to convergence, even under the most favorable choices of price increment for this baseline.

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. We also conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finite-sample analysis. We also propose an accelerated algorithm, called GTD2-MP, that uses proximal "mirror maps" to yield an improved convergence rate. The results of our theoretical analysis imply that the GTD family of algorithms are comparable and may indeed be preferred over existing least squares TD methods for off-policy learning, due to their linear complexity. We provide experimental results showing the improved performance of our accelerated gradient TD methods.