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.

We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that a top-down sensing procedure can identify these partitions, and hence the activations, using few measurements. By exploiting the cluster structure, we are able to provide localization guarantees at weaker signal to noise ratios than in the unstructured setting. We complement this performance guarantee with an information theoretic lower bound, providing a necessary signal-to-noise ratio for any algorithm to successfully localize the cluster. We verify our analysis with some simulations, demonstrating the practicality of our algorithm.

We present a comprehensive study on the use of autoencoders for modelling text data, in which (differently from previous studies) we focus our attention on the following issues: i) we explore the suitability of two different models bDA and rsDA for constructing deep autoencoders for text data at the sentence level; ii) we propose and evaluate two novel metrics for better assessing the text-reconstruction capabilities of autoencoders; and iii) we propose an automatic method to find the critical bottleneck dimensionality for text language representations (below which structural information is lost).

The potential of recovering the topology of a grid using solely publicly available market data is explored here. In contemporary whole-sale electricity markets, real-time prices are typically determined by solving the network-constrained economic dispatch problem. Under a linear DC model, locational marginal prices (LMPs) correspond to the Lagrange multipliers of the linear program involved. The interesting observation here is that the matrix of spatiotemporally varying LMPs exhibits the following property: Once premultiplied by the weighted grid Laplacian, it yields a low-rank and sparse matrix. Leveraging this rich structure, a regularized maximum likelihood estimator (MLE) is developed to recover the grid Laplacian from the LMPs. The convex optimization problem formulated includes low rank- and sparsity-promoting regularizers, and it is solved using a scalable algorithm. Numerical tests on prices generated for the IEEE 14-bus benchmark provide encouraging topology recovery results.

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.

The Generalized Traveling Salesman Problem (GTSP) is one of the NP-hard combinatorial optimization problems. A variant of GTSP is E-GTSP where E, meaning equality, has the constraint: exactly one node from a cluster of a graph partition is visited. The main objective of the E-GTSP is to find a minimum cost tour passing through exactly one node from each cluster of an undirected graph. Agent-based approaches involving are successfully used nowadays for solving real life complex problems. The aim of the current paper is to illustrate some variants of agent-based algorithms including ant-based models with specific properties for solving E-GTSP.

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.

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come.