Score calibration enables automatic speaker recognizers to make cost-effective accept / reject decisions. Traditional calibration requires supervised data, which is an expensive resource. We propose a 2-component GMM for unsupervised calibration and demonstrate good performance relative to a supervised baseline on NIST SRE'10 and SRE'12. A Bayesian analysis demonstrates that the uncertainty associated with the unsupervised calibration parameter estimates is surprisingly small.

The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We argue that this is not a conceptually sound approach and suggest an alternative based on the new law of total odds. We quantify the bias of the total probability estimator of the unconditional class probabilities and show that the total odds estimator is unbiased. The sample version of the total odds estimator is shown to coincide with a maximum-likelihood estimator known from the literature. The law of total odds can also be used for transforming the conditional class probabilities if independent estimates of the unconditional class probabilities of the population are available. Keywords: Total probability, likelihood ratio, Bayes' formula, binary classification, relative odds, unbiased estimator, supervised learning, dataset shift.

We present a formal model of human decision-making in explore-exploit tasks using the context of multi-armed bandit problems, where the decision-maker must choose among multiple options with uncertain rewards. We address the standard multi-armed bandit problem, the multi-armed bandit problem with transition costs, and the multi-armed bandit problem on graphs. We focus on the case of Gaussian rewards in a setting where the decision-maker uses Bayesian inference to estimate the reward values. We model the decision-maker's prior knowledge with the Bayesian prior on the mean reward. We develop the upper credible limit (UCL) algorithm for the standard multi-armed bandit problem and show that this deterministic algorithm achieves logarithmic cumulative expected regret, which is optimal performance for uninformative priors. We show how good priors and good assumptions on the correlation structure among arms can greatly enhance decision-making performance, even over short time horizons. We extend to the stochastic UCL algorithm and draw several connections to human decision-making behavior. We present empirical data from human experiments and show that human performance is efficiently captured by the stochastic UCL algorithm with appropriate parameters. For the multi-armed bandit problem with transition costs and the multi-armed bandit problem on graphs, we generalize the UCL algorithm to the block UCL algorithm and the graphical block UCL algorithm, respectively. We show that these algorithms also achieve logarithmic cumulative expected regret and require a sub-logarithmic expected number of transitions among arms. We further illustrate the performance of these algorithms with numerical examples.

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function parameters are usually learned using maximum likelihood, which can lead to overfitting. To address these problems we introduce a novel model for time-changing variances using Gaussian Processes. A Gaussian Process (GP) defines a distribution over functions, which allows us to capture highly flexible functional relationships for the variances. In addition, we develop an online algorithm to perform inference. The algorithm has two main advantages. First, it takes a Bayesian approach, thereby avoiding overfitting. Second, it is much quicker than current offline inference procedures. Finally, our new model was evaluated on financial data and showed significant improvement in predictive performance over current standard models.

We present a method for incorporating missing data in non-parametric statistical learning without the need for imputation. We focus on a tree-based method, Bayesian Additive Regression Trees (BART), enhanced with "Missingness Incorporated in Attributes," an approach recently proposed incorporating missingness into decision trees (Twala, 2008). This procedure takes advantage of the partitioning mechanisms found in tree-based models. Simulations on generated models and real data indicate that our proposed method can forecast well on complicated missing-at-random and not-missing-at-random models as well as models where missingness itself influences the response. Our procedure has higher predictive performance and is more stable than competitors in many cases. We also illustrate BART's abilities to incorporate missingness into uncertainty intervals and to detect the influence of missingness on the model fit.

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' rule, imposing posterior regularization is arguably more direct and in some cases more natural and general. In this paper, we present regularized Bayesian inference (RegBayes), a novel computational framework that performs posterior inference with a regularization term on the desired post-data posterior distribution under an information theoretical formulation. RegBayes is more flexible than the procedure that elicits expert knowledge via priors, and it covers both directed Bayesian networks and undirected Markov networks whose Bayesian formulation results in hybrid chain graph models. When the regularization is induced from a linear operator on the posterior distributions, such as the expectation operator, we present a general convex-analysis theorem to characterize the solution of RegBayes. Furthermore, we present two concrete examples of RegBayes, infinite latent support vector machines (iLSVM) and multi-task infinite latent support vector machines (MT-iLSVM), which explore the large-margin idea in combination with a nonparametric Bayesian model for discovering predictive latent features for classification and multi-task learning, respectively. We present efficient inference methods and report empirical studies on several benchmark datasets, which appear to demonstrate the merits inherited from both large-margin learning and Bayesian nonparametrics. Such results were not available until now, and contribute to push forward the interface between these two important subfields, which have been largely treated as isolated in the community.

The computational costs of inference and planning have confined Bayesian model-based reinforcement learning to one of two dismal fates: powerful Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian non-parametric models but using simple, myopic planning strategies such as Thompson sampling. We ask whether it is feasible and truly beneficial to combine rich probabilistic models with a closer approximation to fully Bayesian planning. First, we use a collection of counterexamples to show formal problems with the over-optimism inherent in Thompson sampling. Then we leverage state-of-the-art techniques in efficient Bayes-adaptive planning and non-parametric Bayesian methods to perform qualitatively better than both existing conventional algorithms and Thompson sampling on two contextual bandit-like problems.

It is the main purpose of this paper to introduce a graph-valued stochastic process in order to model the spread of a communicable infectious disease. The major novelty of the SIR model we promote lies in the fact that the social network on which the epidemics is taking place is not specified in advance but evolves through time, accounting for the temporal evolution of the interactions involving infective individuals. Without assuming the existence of a fixed underlying network model, the stochastic process introduced describes, in a flexible and realistic manner, epidemic spread in non-uniformly mixing and possibly heterogeneous populations. It is shown how to fit such a (parametrised) model by means of Approximate Bayesian Computation methods based on graph-valued statistics. The concepts and statistical methods described in this paper are finally applied to a real epidemic dataset, related to the spread of HIV in Cuba in presence of a contact tracing system, which permits one to reconstruct partly the evolution of the graph of sexual partners diagnosed HIV positive between 1986 and 2006.

One of the most tedious tasks in the application of machine learning is model selection, i.e. hyperparameter selection. Fortunately, recent progress has been made in the automation of this process, through the use of sequential model-based optimization (SMBO) methods. This can be used to optimize a cross-validation performance of a learning algorithm over the value of its hyperparameters. However, it is well known that ensembles of learned models almost consistently outperform a single model, even if properly selected. In this paper, we thus propose an extension of SMBO methods that automatically constructs such ensembles. This method builds on a recently proposed ensemble construction paradigm known as agnostic Bayesian learning. In experiments on 22 regression and 39 classification data sets, we confirm the success of this proposed approach, which is able to outperform model selection with SMBO.

Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples of latent networks include economic interactions linking financial instruments and patterns of reciprocity in gang violence. In these cases, we are limited to noisy observations of events associated with each node. To enable analysis of these implicit networks, we develop a probabilistic model that combines mutually-exciting point processes with random graph models. We show how the Poisson superposition principle enables an elegant auxiliary variable formulation and a fully-Bayesian, parallel inference algorithm. We evaluate this new model empirically on several datasets.