The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the system as the parameter values are varied. This process often encounters two major difficulties: the generation of synthetic data for each considered set of parameter values can be computationally expensive if the system model is complicated; and the exploration of the parameter space can be inefficient and/or incomplete, a typical example being when the exploration becomes trapped in a local optimum of the objection function that characterises the mismatch between the measured and synthetic data. A method to address both these issues is presented, whereby: a surrogate model (or proxy), which emulates the computationally expensive system simulator, is constructed using deep recurrent networks (DRN); and a nested sampling (NS) algorithm is employed to perform efficient and robust exploration of the parameter space. The analysis is performed in a Bayesian context, in which the samples characterise the full joint posterior distribution of the parameters, from which parameter estimates and uncertainties are easily derived. The proposed approach is compared with conventional methods in some numerical examples, for which the results demonstrate that one can accelerate the parameter estimation process by at least an order of magnitude.

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.

The aim of this paper was to compare soft confusion matrix approach and Bayes metaclassifier under the multi-label classification framework. Although the methods were successfully applied under the multi-label classification framework, they have not been compared directly thus far. Such comparison is of vital importance because both methods are quite similar as they are both based on the concept of randomized reference classifier. Since both algorithms were designed to deal with single-label problems, they are combined with the problem-transformation approach to multi-label classification. Present study included 29 benchmark datasets and four different base classifiers. The algorithms were compared in terms of 11 quality criteria and the results were subjected to statistical analysis.

Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support of the inverse covariance matrix corresponds to the edges of the graphical model. Instead, suppose we only have noisy observations. If the noise at each node is independent, we can compute the sum of the covariance matrix and an unknown diagonal. The inverse of this sum is (in general) dense. We ask: can the original independence structure be recovered? We address this question for tree structured graphical models. We prove that this problem is unidentifiable, but show that this unidentifiability is limited to a small class of candidate trees. We further present additional constraints under which the problem is identifiable. Finally, we provide an O(n^3) algorithm to find this equivalence class of trees.

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.

The current state-of-the-art Scrabble agents are not learning-based but depend on truncated Monte Carlo simulations and the quality of such agents is contingent upon the time available for running the simulations. This thesis takes steps towards building a learning-based Scrabble agent using self-play. Specifically, we try to find a better function approximation for the static evaluation function used in Scrabble which determines the move goodness at a given board configuration. In this work, we experimented with evolutionary algorithms and Bayesian Optimization to learn the weights for an approximate feature-based evaluation function. However, these optimization methods were not quite effective, which lead us to explore the given problem from an Imitation Learning point of view. We also tried to imitate the ranking of moves produced by the Quackle simulation agent using supervised learning with a neural network function approximator which takes the raw representation of the Scrabble board as the input instead of using only a fixed number of handcrafted features.