Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this estimation problem efficiently using graphical models, which is particularly effective when the distribution is high-dimensional but the measurements are over low-dimensional marginals. We show that our approach is far more efficient than existing estimation techniques from the privacy literature and that it can improve the accuracy and scalability of many state-of-the-art mechanisms.

Abstract--Market research is generally performed by surveying arepresentative sample of customers with questions that includes contexts such as psycho-graphics, demographics, attitude and product preferences. Survey responses are used to segment the customers into various groups that are useful for targeted marketing and communication. Reducing the number of questions asked to the customer has utility for businesses to scale the market research to a large number of customers. We demonstrate the effectiveness of our approach using an example market segmentation of broadband customers. I. INTRODUCTION A key technique for developing successful business strategies inbusiness to customer (B2C) companies is to develop a good understanding of the market and the customer behavior.

Parameter estimation of unnormalized models is a challenging problem because normalizing constants are not calculated explicitly and maximum likelihood estimation is computationally infeasible. Although some consistent estimators have been proposed earlier, the problem of statistical efficiency does remain. In this study, we propose a unified, statistically efficient estimation framework for unnormalized models and several novel efficient estimators with reasonable computational time regardless of whether the sample space is discrete or continuous. The loss functions of the proposed estimators are derived by combining the following two methods: (1) density-ratio matching using Bregman divergence, and (2) plugging-in nonparametric estimators. We also analyze the properties of the proposed estimators when the unnormalized model is misspecified. Finally, the experimental results demonstrate the advantages of our method over existing approaches.

The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and hence the model capacity can be controlled. The algorithmic infrastructure is developed based on the synthesis and analysis prior models whose rate-distortion properties, as well as capacity vs. sample complexity trade-offs are carefully optimized. These models are then extended to multi-layers, namely the RRQ and the ML-STC frameworks, where the latter is further evolved as a powerful deep neural network architecture with fast and sample-efficient training and discrete representations. For the developed algorithms, three important applications are developed. First, the problem of large-scale similarity search in retrieval systems is addressed, where a double-stage solution is proposed leading to faster query times and shorter database storage. Second, the problem of learned image compression is targeted, where the proposed models can capture more redundancies from the training images than the conventional compression codecs. Finally, the proposed algorithms are used to solve ill-posed inverse problems. In particular, the problems of image denoising and compressive sensing are addressed with promising results.

Recovering pairwise interactions, i.e. pairs of input features whose joint effect on an output is different from the sum of their marginal effects, is central in many scientific applications. We conceptualize a solution to this problem as a two-stage procedure: first, we model the relationship between the features and the output using a flexible hybrid neural network; second, we detect feature interactions from the trained model. For the second step we propose a simple and intuitive interaction measure (IM), which has no specific requirements on the machine learning model used in the first step, only that it defines a mapping from an input to an output. And in a special case it reduces to the averaged Hessian of the input-output mapping. Importantly, our method upper bounds the interaction recovery error with the error of the learning model, which ensures that we can improve the recovered interactions by training a more accurate model. We present analyses of simulated and real-world data which demonstrate the benefits of our method compared to available alternatives, and theoretically analyse its properties and relation to other methods.

We report on an empirical study of the main strategies for conditional quantile estimation in the context of stochastic computer experiments. To ensure adequate diversity, six metamodels are presented, divided into three categories based on order statistics, functional approaches, and those of Bayesian inspiration. The metamodels are tested on several problems characterized by the size of the training set, the input dimension, the quantile order and the value of the probability density function in the neighborhood of the quantile. The metamodels studied reveal good contrasts in our set of 480 experiments, enabling several patterns to be extracted. Based on our results, guidelines are proposed to allow users to select the best method for a given problem.

Next-generation wireless networks (NGWN) have a substantial potential in terms of supporting a broad range of complex compelling applications both in military and civilian fields, where the users are able to enjoy high-rate, low-latency, low-cost and reliable information services. Achieving this ambitious goal requires new radio techniques for adaptive learning and intelligent decision making because of the complex heterogeneous nature of the network structures and wireless services. Machine learning algorithms have great success in supporting big data analytics, efficient parameter estimation and interactive decision making. Hence, in this article, we review the thirty-year history of machine learning by elaborating on supervised learning, unsupervised learning, reinforcement learning and deep learning, respectively. Furthermore, we investigate their employment in the compelling applications of NGWNs, including heterogeneous networks (HetNets), cognitive radios (CR), Internet of things (IoT), machine to machine networks (M2M), and so on. This article aims for assisting the readers in clarifying the motivation and methodology of the various machine learning algorithms, so as to invoke them for hitherto unexplored services as well as scenarios of future wireless networks.

We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a directed acyclic graph (DAG) and the associated joint probability distribution of the nodes consistent with a given dataset. This is a combinatorial problem of structural learning of the underlying graph, starting from a single node and building one arc at a time, that fits a given ensemble using maximum likelihood estimators (MLE). It is cast as an optimization problem that consists of a scoring step performed on a classical computer, penalties for acyclicity and number of parents allowed constraints, and a search step implemented using a quantum annealer. We have assumed uniform priors in deriving the Bayesian network that can be relaxed by formulating the problem as an estimation Dirichlet parameters. We demonstrate the utility of the framework by applying to the problem of elucidating the gene regulatory network for the MAPK/Raf pathway in human T-cells using proteomics data where the concentration of proteins, nodes of the BN, are interpreted as probabilities.

Autoencoders are a deep learning model for representation learning. When trained to minimize the Euclidean distance between the data and its reconstruction, linear autoencoders (LAEs) learn the subspace spanned by the top principal directions but cannot learn the principal directions themselves. In this paper, we prove that $L_2$-regularized LAEs learn the principal directions as the left singular vectors of the decoder, providing an extremely simple and scalable algorithm for rank-$k$ SVD. More generally, we consider LAEs with (i) no regularization, (ii) regularization of the composition of the encoder and decoder, and (iii) regularization of the encoder and decoder separately. We relate the minimum of (iii) to the MAP estimate of probabilistic PCA and show that for all critical points the encoder and decoder are transposes. Building on topological intuition, we smoothly parameterize the critical manifolds for all three losses via a novel unified framework and illustrate these results empirically. Overall, this work clarifies the relationship between autoencoders and Bayesian models and between regularization and orthogonality.

We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization and stabilization of training procedures, and also can parameterize matrices of bounded rank, positive-definite matrices and others. In \citet{byrne2013geodesic} authors have already considered sampling from distributions over manifolds using exact geodesic flows in a scheme similar to Hamiltonian Monte Carlo (HMC). We propose new sampling scheme for a set of orthogonal matrices that is based on the same approach, uses ideas of Riemannian optimization and does not require exact computation of geodesic flows. The method is theoretically justified by proof of symplecticity for the proposed iteration. In experiments we show that the new scheme is comparable or faster in time per iteration and more sample-efficient comparing to conventional HMC with explicit orthogonal parameterization and Geodesic Monte-Carlo. We also provide promising results of Bayesian ensembling for orthogonal neural networks and low-rank matrix factorization.