Domain generalization is the problem of assigning class labels to an unlabeled test data set, given several labeled training data sets drawn from similar distributions. This problem arises in several applications where data distributions fluctuate because of biological, technical, or other sources of variation. We develop a distribution-free, kernel-based approach that predicts a classifier from the marginal distribution of features, by leveraging the trends present in related classification tasks. This approach involves identifying an appropriate reproducing kernel Hilbert space and optimizing a regularized empirical risk over the space. We present generalization error analysis, describe universal kernels, and establish universal consistency of the proposed methodology. Experimental results on synthetic data and three real data applications demonstrate the superiority of the method with respect to a pooling strategy.

The EM algorithm is one of many important tools in the field of statistics. While often used for imputing missing data, its widespread applications include other common statistical tasks, such as clustering. In clustering, the EM algorithm assumes a parametric distribution for the clusters, whose parameters are estimated through a novel iterative procedure that is based on the theory of maximum likelihood. However, one major drawback of the EM algorithm, that renders it impractical especially when working with large datasets, is that it often requires several passes of the data before convergence. In this paper, we introduce a new EM-style algorithm that implements a novel policy for performing partial E-steps. We call the new algorithm the EM-Tau algorithm, which can approximate the traditional EM algorithm with high accuracy but with only a fraction of the running time.

We propose an approach to reduce both computational complexity and data storage requirements for the online positioning stage of a fingerprinting-based indoor positioning system (FIPS) by introducing segmentation of the region of interest (RoI) into sub-regions, sub-region selection using a modified Jaccard index, and feature selection based on randomized least absolute shrinkage and selection operator (LASSO). We implement these steps into a Bayesian framework of position estimation using the maximum a posteriori (MAP) principle. An additional benefit of these steps is that the time for estimating the position, and the required data storage are virtually independent of the size of the RoI and of the total number of available features within the RoI. Thus the proposed steps facilitate application of FIPS to large areas. Results of an experimental analysis using real data collected in an office building using a Nexus 6P smart phone as user device and a total station for providing position ground truth corroborate the expected performance of the proposed approach. The positioning accuracy obtained by only processing 10 automatically identified features instead of all available ones and limiting position estimation to 10 automatically identified sub-regions instead of the entire RoI is equivalent to processing all available data. In the chosen example, 50% of the errors are less than 1.8 m and 90% are less than 5 m. However, the computation time using the automatically identified subset of data is only about 1% of that required for processing the entire data set.

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form --- where form could be a tree, ring, chain, grid, etc. [Kemp & Tenenbaum (2008). The discovery of structural form. PNAS, 105(3), 10687-10692]. While this approach can learn intuitive organizations, including a tree for animals and a ring for the color circle, it assumes a strong inductive bias that considers only these particular forms, and each form is explicitly provided as initial knowledge. Here we introduce a new computational model of how organizing structure can be discovered, utilizing a broad hypothesis space with a preference for sparse connectivity. Given that the inductive bias is more general, the model's initial knowledge shows little qualitative resemblance to some of the discoveries it supports. As a consequence, the model can also learn complex structures for domains that lack intuitive description, as well as predict human property induction judgments without explicit structural forms. By allowing form to emerge from sparsity, our approach clarifies how both the richness and flexibility of human conceptual organization can coexist.

Predicting epidemic dynamics is of great value in understanding and controlling diffusion processes, such as infectious disease spread and information propagation. This task is intractable, especially when surveillance resources are very limited. To address the challenge, we study the problem of active surveillance, i.e., how to identify a small portion of system components as sentinels to effect monitoring, such that the epidemic dynamics of an entire system can be readily predicted from the partial data collected by such sentinels. We propose a novel measure, the gamma value, to identify the sentinels by modeling a sentinel network with row sparsity structure. We design a flexible group sparse Bayesian learning algorithm to mine the sentinel network suitable for handling both linear and non-linear dynamical systems by using the expectation maximization method and variational approximation. The efficacy of the proposed algorithm is theoretically analyzed and empirically validated using both synthetic and real-world data.

A major target of linguistics and cognitive science has been to understand what class of learning systems can acquire the key structures of natural language. Until recently, the computational requirements of language have been used to argue that learning is impossible without a highly constrained hypothesis space. Here, we describe a learning system that is maximally unconstrained, operating over the space of all computations, and is able to acquire several of the key structures present natural language from positive evidence alone. The model successfully acquires regular (e.g. $(ab)^n$), context-free (e.g. $a^n b^n$, $x x^R$), and context-sensitive (e.g. $a^nb^nc^n$, $a^nb^mc^nd^m$, $xx$) formal languages. Our approach develops the concept of factorized programs in Bayesian program induction in order to help manage the complexity of representation. We show in learning, the model predicts several phenomena empirically observed in human grammar acquisition experiments.

Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population genetics, ecology or network analysis. While the exchangeability assumption is sensible in many cases, it has some strong implications. In particular, Kingman's representation theorem implies that the size of the clusters necessarily grows linearly with the sample size; this feature may be undesirable for some applications, as recently pointed out by Miller et al. (2015). We present here a flexible class of non-exchangeable random partition models which are able to generate partitions whose cluster sizes grow sublinearly with the sample size, and where the growth rate is controlled by one parameter. Along with this result, we provide the asymptotic behaviour of the number of clusters of a given size, and show that the model can exhibit a power-law behavior, controlled by another parameter. The construction is based on completely random measures and a Poisson embedding of the random partition, and inference is performed using a Sequential Monte Carlo algorithm. Additionally, we show how the model can also be directly used to generate sparse multigraphs with power-law degree distributions and degree sequences with sublinear growth. Finally, experiments on real datasets emphasize the usefulness of the approach compared to a two-parameter Chinese restaurant process.

Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since the ELBO requires variational likelihood evaluations of the latent variables. In this paper, we propose a novel framework to enrich the variational family based on an alternative lower bound, by introducing auxiliary random variables to the variational distribution only. While offering a much richer family of complex variational distributions, the resulting inference network is likelihood almost free in the sense that only the latent variables require evaluations from simple likelihoods and samples from all the auxiliary variables are sufficient for maximum likelihood inference. We show that the proposed approach is essentially optimizing a probabilistic mixture of ELBOs, thus enriching modeling capacity and enhancing robustness. It outperforms state-of-the-art methods in our experiments on several density estimation tasks.

Inpatient care is a large share of total health care spending, making analysis of inpatient utilization patterns an important part of understanding what drives health care spending growth. Common features of inpatient utilization measures include zero inflation, over-dispersion, and skewness, all of which complicate statistical modeling. Mixture modeling is a popular approach that can accommodate these features of health care utilization data. In this work, we add a nonparametric clustering component to such models. Our fully Bayesian model framework allows for an unknown number of mixing components, so that the data determine the number of mixture components. When we apply the modeling framework to data on hospital lengths of stay for patients with lung cancer, we find distinct subgroups of patients with differences in means and variances of hospital days, health and treatment covariates, and relationships between covariates and length of stay.

Non-negative matrix factorization (NMF) is a technique for finding latent representations of data. The method has been applied to corpora to construct topic models. However, NMF has likelihood assumptions which are often violated by real document corpora. We present a double parametric bootstrap test for evaluating the fit of an NMF-based topic model based on the duality of the KL divergence and Poisson maximum likelihood estimation. The test correctly identifies whether a topic model based on an NMF approach yields reliable results in simulated and real data.