Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that explicitly models the empirical population distribution as part of Bayesian analysis. We introduce a new concept, the latent dataset, as a hierarchical variable and set the empirical population as its prior. This leads to a new predictive density that mitigates model mismatch. We efficiently apply this method to complex models by proposing a stochastic variational inference algorithm, called bumping variational inference (BUMP-VI). We demonstrate improved predictive accuracy over classical Bayesian inference in three models: a linear regression model of health data, a Bayesian mixture model of natural images, and a latent Dirichlet allocation topic model of scientific documents.

An active learner is given a class of models, a large set of unlabeled examples, and the ability to interactively query labels of a subset of these examples; the goal of the learner is to learn a model in the class that fits the data well. Previous theoretical work has rigorously characterized label complexity of active learning, but most of this work has focused on the PAC or the agnostic PAC model. In this paper, we shift our attention to a more general setting -- maximum likelihood estimation. Provided certain conditions hold on the model class, we provide a two-stage active learning algorithm for this problem. The conditions we require are fairly general, and cover the widely popular class of Generalized Linear Models, which in turn, include models for binary and multi-class classification, regression, and conditional random fields. We provide an upper bound on the label requirement of our algorithm, and a lower bound that matches it up to lower order terms. Our analysis shows that unlike binary classification in the realizable case, just a single extra round of interaction is sufficient to achieve near-optimal performance in maximum likelihood estimation. On the empirical side, the recent work in ~\cite{Zhang12} and~\cite{Zhang14} (on active linear and logistic regression) shows the promise of this approach.

We investigate the systematic mechanism for designing fast mixing Markov chain Monte Carlo algorithms to sample from discrete point processes under the Dobrushin uniqueness condition for Gibbs measures. Discrete point processes are defined as probability distributions $\mu(S)\propto \exp(\beta f(S))$ over all subsets $S\in 2^V$ of a finite set $V$ through a bounded set function $f:2^V\rightarrow \mathbb{R}$ and a parameter $\beta>0$. A subclass of discrete point processes characterized by submodular functions (which include log-submodular distributions, submodular point processes, and determinantal point processes) has recently gained a lot of interest in machine learning and shown to be effective for modeling diversity and coverage. We show that if the set function (not necessarily submodular) displays a natural notion of decay of correlation, then, for $\beta$ small enough, it is possible to design fast mixing Markov chain Monte Carlo methods that yield error bounds on marginal approximations that do not depend on the size of the set $V$. The sufficient conditions that we derive involve a control on the (discrete) Hessian of set functions, a quantity that has not been previously considered in the literature. We specialize our results for submodular functions, and we discuss canonical examples where the Hessian can be easily controlled.

BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of implementing the variational Bayesian update equations, the user can construct models faster and in a less error-prone way. Simple syntax, flexible model construction and efficient inference make BayesPy suitable for both average and expert Bayesian users. It also supports some advanced methods such as stochastic and collapsed variational inference.

Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) approach to overcome these limitations. We derive the small-variance asymptotics for parametric and nonparametric MJPs for both directly observed and hidden state models. In the parametric case we obtain a novel objective function which leads to non-degenerate trajectories. To derive the nonparametric version we introduce the gamma-gamma process, a novel extension to the gamma-exponential process. We propose algorithms for each of these formulations, which we call \emph{JUMP-means}. Our experiments demonstrate that JUMP-means is competitive with or outperforms widely used MJP inference approaches in terms of both speed and reconstruction accuracy.

There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the autoencoder's parameters to respect autoregressive constraints: each input is reconstructed only from previous inputs in a given ordering. Constrained this way, the autoencoder outputs can be interpreted as a set of conditional probabilities, and their product, the full joint probability. We can also train a single network that can decompose the joint probability in multiple different orderings. Our simple framework can be applied to multiple architectures, including deep ones. Vectorized implementations, such as on GPUs, are simple and fast. Experiments demonstrate that this approach is competitive with state-of-the-art tractable distribution estimators. At test time, the method is significantly faster and scales better than other autoregressive estimators.

We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure. The main challenge with learning parameters of such models is that iterative methods such as EM are very slow, while naive spectral methods result in time and space complexity exponential in the number of cell types. We exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets. We provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types. Finally, we show that beyond our specific model, some of our algorithmic ideas can be applied to other graphical models.

Preference learning (PL) is a core area of machine learning that handles datasets with ordinal relations. As the number of generated data of ordinal nature is increasing, the importance and role of the PL field becomes central within machine learning research and practice. This paper introduces an open source, scalable, efficient and accessible preference learning toolbox that supports the key phases of the data training process incorporating various popular data preprocessing, feature selection and preference learning methods.

Joint peak detection is a central problem when comparing samples in genomic data analysis, but current algorithms for this task are unsupervised and limited to at most 2 sample types. We propose PeakSegJoint, a new constrained maximum likelihood segmentation model for any number of sample types. To select the number of peaks in the segmentation, we propose a supervised penalty learning model. To infer the parameters of these two models, we propose to use a discrete optimization heuristic for the segmentation, and convex optimization for the penalty learning. In comparisons with state-of-the-art peak detection algorithms, PeakSegJoint achieves similar accuracy, faster speeds, and a more interpretable model with overlapping peaks that occur in exactly the same positions across all samples.

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality.