This paper investigates asymptotic properties of a class of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the mean, such as the median-of-means estimator. It is well known by now that the excess risk of resulting estimators often converges to 0 at the optimal rates under much weaker assumptions than those required by their "classical" counterparts. However, much less is known about asymptotic properties of the estimators themselves, for instance, whether robust analogues of the maximum likelihood estimators are asymptotically efficient. We make a step towards answering these questions and show that for a wide class of parametric problems, minimizers of the appropriately defined robust proxy of the risk converge to the minimizers of the true risk at the same rate, and often have the same asymptotic variance, as the estimators obtained by minimizing the usual empirical risk. Moreover, our results show that robust algorithms based on the so-called "min-max" type procedures in many cases provably outperform, is the asymptotic sense, algorithms based on direct risk minimization.

Diagnosing problems in Internet-scale services remains particularly difficult and costly for both content providers and ISPs. Because the Internet is decentralized, the cause of such problems might lie anywhere between an end-user's device and the service datacenters. Further, the set of possible problems and causes is not known in advance, making it impossible in practice to train a classifier with all combinations of problems, causes and locations. In this paper, we explore how different machine learning techniques can be used for Internet-scale root cause analysis using measurements taken from end-user devices. We show how to build generic models that (i) are agnostic to the underlying network topology, (ii) do not require to define the full set of possible causes during training, and (iii) can be quickly adapted to diagnose new services. Our solution, DiagNet, adapts concepts from image processing research to handle network and system metrics. We evaluate DiagNet with a multi-cloud deployment of online services with injected faults and emulated clients with automated browsers. We demonstrate promising root cause analysis capabilities, with a recall of 73.9% including causes only being introduced at inference time.

Recursive Bayesian inference (RBI) provides optimal Bayesian latent variable estimates in real-time settings with streaming noisy observations. Active RBI attempts to effectively select queries that lead to more informative observations to rapidly reduce uncertainty until a confident decision is made. However, typically the optimality objectives of inference and query mechanisms are not jointly selected. Furthermore, conventional active querying methods stagger due to misleading prior information. Motivated by information theoretic approaches, we propose an active RBI framework with unified inference and query selection steps through Renyi entropy and $\alpha$-divergence. We also propose a new objective based on Renyi entropy and its changes called Momentum that encourages exploration for misleading prior cases. The proposed active RBI framework is applied to the trajectory of the posterior changes in the probability simplex that provides a coordinated active querying and decision making with specified confidence. Under certain assumptions, we analytically demonstrate that the proposed approach outperforms conventional methods such as mutual information by allowing the selections of unlikely events. We present empirical and experimental performance evaluations on two applications: restaurant recommendation and brain-computer interface (BCI) typing systems.

The mixture extension of exponential family principal component analysis (EPCA) was designed to encode much more structural information about data distribution than the traditional EPCA does. For example, due to the linearity of EPCA's essential form, nonlinear cluster structures cannot be easily handled, but they are explicitly modeled by the mixing extensions. However, the traditional mixture of local EPCAs has the problem of model redundancy, i.e., overlaps among mixing components, which may cause ambiguity for data clustering. To alleviate this problem, in this paper, a repulsiveness-encouraging prior is introduced among mixing components and a diversified EPCA mixture (DEPCAM) model is developed in the Bayesian framework. Specifically, a determinantal point process (DPP) is exploited as a diversity-encouraging prior distribution over the joint local EPCAs. As required, a matrix-valued measure for L-ensemble kernel is designed, within which, $\ell_1$ constraints are imposed to facilitate selecting effective PCs of local EPCAs, and angular based similarity measure are proposed. An efficient variational EM algorithm is derived to perform parameter learning and hidden variable inference. Experimental results on both synthetic and real-world datasets confirm the effectiveness of the proposed method in terms of model parsimony and generalization ability on unseen test data.

The Gaussian process (GP) is an attractive Bayesian model for machine learning which combines an elegant formulation with model flexibility and uncertainty quantification. Sparse Gaussian process (sGP) algorithms provide an approximate solution that mitigates the high computational complexity of GP and the variational approximation is the current best practice for such approximations. Recent theoretical work has shown that an alternative approach, direct loss minimization (DLM), which directly minimizes predictive loss, comes with strong guarantees on the expected loss of the algorithm. In this paper we explore this approach experimentally. We develop the DLM algorithm for sGP and show that with appropriate hyperparameter optimization it provides a significant improvement over the variational approach. In particular, optimizing sGP for log loss provides better calibrated predictions for regression, classification and count prediction, and optimizing sGP for square loss improves the mean square error in regression.

Matrix factorization is a very common machine learning technique in recommender systems. Bayesian Matrix Factorization (BMF) algorithms would be attractive because of their ability to quantify uncertainty in their predictions and avoid over-fitting, combined with high prediction accuracy. However, they have not been widely used on large-scale data because of their prohibitive computational cost. In recent work, efforts have been made to reduce the cost, both by improving the scalability of the BMF algorithm as well as its implementation, but so far mainly separately. In this paper we show that the state-of-the-art of both approaches to scalability can be combined. We combine the recent highly-scalable Posterior Propagation algorithm for BMF, which parallelizes computation of blocks of the matrix, with a distributed BMF implementation that users asynchronous communication within each block. We show that the combination of the two methods gives substantial improvements in the scalability of BMF on web-scale datasets, when the goal is to reduce the wall-clock time.

Bayesian deep neural networks (DNN) provide a mathematically grounded framework to quantify uncertainty in their predictions. We propose a Bayesian variant of policy-gradient based reinforcement learning training technique for image captioning models to directly optimize non-differentiable image captioning quality metrics such as CIDEr-D. We extend the well-known Self-Critical Sequence Training (SCST) approach for image captioning models by incorporating Bayesian inference, and refer to it as B-SCST. The "baseline" reward for the policy-gradients in B-SCST is generated by averaging predictive quality metrics (CIDEr-D) of the captions drawn from the distribution obtained using a Bayesian DNN model. This predictive distribution is inferred using Monte Carlo (MC) dropout, which is one of the standard ways to approximate variational inference. We observe that B-SCST improves all the standard captioning quality scores on both Flickr30k and MS COCO datasets, compared to the SCST approach. We also provide a detailed study of uncertainty quantification for the predicted captions, and demonstrate that it correlates well with the CIDEr-D scores. To our knowledge, this is the first such analysis, and it can pave way to more practical image captioning solutions with interpretable models.

In this paper we consider the problem of computing the likelihood of the profile of a discrete distribution, i.e., the probability of observing the multiset of element frequencies, and computing a profile maximum likelihood (PML) distribution, i.e., a distribution with the maximum profile likelihood. For each problem we provide polynomial time algorithms that given $n$ i.i.d.\ samples from a discrete distribution, achieve an approximation factor of $\exp\left(-O(\sqrt{n} \log n) \right)$, improving upon the previous best-known bound achievable in polynomial time of $\exp(-O(n^{2/3} \log n))$ (Charikar, Shiragur and Sidford, 2019). Through the work of Acharya, Das, Orlitsky and Suresh (2016), this implies a polynomial time universal estimator for symmetric properties of discrete distributions in a broader range of error parameter. We achieve these results by providing new bounds on the quality of approximation of the Bethe and Sinkhorn permanents (Vontobel, 2012 and 2014). We show that each of these are $\exp(O(k \log(N/k)))$ approximations to the permanent of $N \times N$ matrices with non-negative rank at most $k$, improving upon the previous known bounds of $\exp(O(N))$. To obtain our results on PML, we exploit the fact that the PML objective is proportional to the permanent of a certain Vandermonde matrix with $\sqrt{n}$ distinct columns, i.e. with non-negative rank at most $\sqrt{n}$. As a by-product of our work we establish a surprising connection between the convex relaxation in prior work (CSS19) and the well-studied Bethe and Sinkhorn approximations.

This research work deals with Natural Language Processing (NLP) and extraction of essential information in an explicit form. The most common among the information management strategies is Document Retrieval (DR) and Information Filtering. DR systems may work as combine harvesters, which bring back useful material from the vast fields of raw material. With large amount of potentially useful information in hand, an Information Extraction (IE) system can then transform the raw material by refining and reducing it to a germ of original text. A Document Retrieval system collects the relevant documents carrying the required information, from the repository of texts. An IE system then transforms them into information that is more readily digested and analyzed. It isolates relevant text fragments, extracts relevant information from the fragments, and then arranges together the targeted information in a coherent framework. The thesis presents a new approach for Word Sense Disambiguation using thesaurus. The illustrative examples supports the effectiveness of this approach for speedy and effective disambiguation. A Document Retrieval method, based on Fuzzy Logic has been described and its application is illustrated. A question-answering system describes the operation of information extraction from the retrieved text documents. The process of information extraction for answering a query is considerably simplified by using a Structured Description Language (SDL) which is based on cardinals of queries in the form of who, what, when, where and why. The thesis concludes with the presentation of a novel strategy based on Dempster-Shafer theory of evidential reasoning, for document retrieval and information extraction. This strategy permits relaxation of many limitations, which are inherent in Bayesian probabilistic approach.

Convergence rate of training algorithms for neural networks is heavily affected by initialization of weights. In this paper, an original algorithm for initialization of weights in backpropagation neural net is presented with application to character recognition. The initialization method is mainly based on a customization of the Kalman filter, translating it into Bayesian statistics terms. A metrological approach is used in this context considering weights as measurements modeled by mutually dependent normal random variables. The algorithm performance is demonstrated by reporting and discussing results of simulation trials. Results are compared with random weights initialization and other methods. The proposed method shows an improved convergence rate for the backpropagation training algorithm.