Models for aggregating contributions by crowd workers have been shown to be challenged by the rise of task-specific biases or errors. Task-dependent errors in assessment may shift the majority opinion of even large numbers of workers to an incorrect answer. We introduce and evaluate probabilistic models that can detect and correct task-dependent bias automatically. First, we show how to build and use probabilistic graphical models for jointly modeling task features, workers' biases, worker contributions and ground truth answers of tasks so that task-dependent bias can be corrected. Second, we show how the approach can perform a type of transfer learning among workers to address the issue of annotation sparsity. We evaluate the models with varying complexity on a large data set collected from a citizen science project and show that the models are effective at correcting the task-dependent worker bias. Finally, we investigate the use of active learning to guide the acquisition of expert assessments to enable automatic detection and correction of worker bias.

In this paper, we propose a model-based clustering method (TVClust) that robustly incorporates noisy side information as soft-constraints and aims to seek a consensus between side information and the observed data. Our method is based on a nonparametric Bayesian hierarchical model that combines the probabilistic model for the data instance and the one for the side-information. An efficient Gibbs sampling algorithm is proposed for posterior inference. Using the small-variance asymptotics of our probabilistic model, we then derive a new deterministic clustering algorithm (RDP-means). It can be viewed as an extension of K-means that allows for the inclusion of side information and has the additional property that the number of clusters does not need to be specified a priori. Empirical studies have been carried out to compare our work with many constrained clustering algorithms from the literature on both a variety of data sets and under a variety of conditions such as using noisy side information and erroneous k values. The results of our experiments show strong results for our probabilistic and deterministic approaches under these conditions when compared to other algorithms in the literature.

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic simulations. However, such stochastic gradient MCMC samplers have lagged behind their full-data counterparts in terms of the complexity of dynamics considered since proving convergence in the presence of the stochastic gradient noise is non-trivial. Even with simple dynamics, significant physical intuition is often required to modify the dynamical system to account for the stochastic gradient noise. In this paper, we provide a general recipe for constructing MCMC samplers--including stochastic gradient versions--based on continuous Markov processes specified via two matrices. We constructively prove that the framework is complete. That is, any continuous Markov process that provides samples from the target distribution can be written in our framework. We show how previous continuous-dynamic samplers can be trivially "reinvented" in our framework, avoiding the complicated sampler-specific proofs. We likewise use our recipe to straightforwardly propose a new state-adaptive sampler: stochastic gradient Riemann Hamiltonian Monte Carlo (SGRHMC). Our experiments on simulated data and a streaming Wikipedia analysis demonstrate that the proposed SGRHMC sampler inherits the benefits of Riemann HMC, with the scalability of stochastic gradient methods.

Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. This paper explores an alternative notion of a tractable set, namely a set of "fast-mixing parameters" where Markov chain Monte Carlo (MCMC) inference can be guaranteed to quickly converge to the stationary distribution. While it is common in practice to approximate the likelihood gradient using samples obtained from MCMC, such procedures lack theoretical guarantees. This paper proves that for any exponential family with bounded sufficient statistics, (not just graphical models) when parameters are constrained to a fast-mixing set, gradient descent with gradients approximated by sampling will approximate the maximum likelihood solution inside the set with high-probability. When unregularized, to find a solution epsilon-accurate in log-likelihood requires a total amount of effort cubic in 1/epsilon, disregarding logarithmic factors. When ridge-regularized, strong convexity allows a solution epsilon-accurate in parameter distance with effort quadratic in 1/epsilon. Both of these provide of a fully-polynomial time randomized approximation scheme.

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem over an appropriately selected family of distributions. The goal is two-fold. Firstly, to find lower-dimensional representations of the unknown parameter vector that capture as much as possible of the associated posterior density, and secondly to enable the computation of the approximate posterior density with as few forward calls as possible. We discuss how these objectives can be achieved by using a fully Bayesian argumentation and employing the marginal likelihood or evidence as the ultimate model validation metric for any proposed dimensionality reduction. We demonstrate the performance of the proposed methodology for problems in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. An Importance Sampling scheme is finally employed in order to validate the results and assess the efficacy of the approximations provided.

In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matching expectations between two models, but sometimes both models are most conveniently expressed as latent variable models. We propose latent Bayesian melding, which is motivated by averaging the distributions over populations statistics of both the individual-level and the population-level models under a logarithmic opinion pool framework. In a case study on electricity disaggregation, which is a type of single-channel blind source separation problem, we show that latent Bayesian melding leads to significantly more accurate predictions than an approach based solely on generalized moment matching.

Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations (SDEs). These SDEs are guaranteed to leave invariant the required posterior distribution. An area of current research addresses the computational benefits of stochastic gradient methods in this setting. Existing techniques rely on estimating the variance or covariance of the subsampling error, and typically assume constant variance. In this article, we propose a covariance-controlled adaptive Langevin thermostat that can effectively dissipate parameter-dependent noise while maintaining a desired target distribution. The proposed method achieves a substantial speedup over popular alternative schemes for large-scale machine learning applications.

#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains (quantitative information flow, static analysis of probabilistic programs). In this paper, we show a reduction from an approximate version of #SMT to SMT. We focus on the theories of integer arithmetic and linear real arithmetic. We propose model counting algorithms that provide approximate solutions with formal bounds on the approximation error. They run in polynomial time and make a polynomial number of queries to the SMT solver for the underlying theory, exploiting "for free" the sophisticated heuristics implemented within modern SMT solvers. We have implemented the algorithms and used them to solve the value problem for a model of loop-free probabilistic programs with nondeterminism.

In this paper, we present $\ell_{1,p}$ multi-task structure learning for Gaussian graphical models. We analyze the sufficient number of samples for the correct recovery of the support union and edge signs. We also analyze the necessary number of samples for any conceivable method by providing information-theoretic lower bounds. We compare the statistical efficiency of multi-task learning versus that of single-task learning. For experiments, we use a block coordinate descent method that is provably convergent and generates a sequence of positive definite solutions. We provide experimental validation on synthetic data as well as on two publicly available real-world data sets, including functional magnetic resonance imaging and gene expression data.

A system is presented that segments, clusters and predicts musical audio in an unsupervised manner, adjusting the number of (timbre) clusters instantaneously to the audio input. A sequence learning algorithm adapts its structure to a dynamically changing clustering tree. The flow of the system is as follows: 1) segmentation by onset detection, 2) timbre representation of each segment by Mel frequency cepstrum coefficients, 3) discretization by incremental clustering, yielding a tree of different sound classes (e.g. instruments) that can grow or shrink on the fly driven by the instantaneous sound events, resulting in a discrete symbol sequence, 4) extraction of statistical regularities of the symbol sequence, using hierarchical N-grams and the newly introduced conceptual Boltzmann machine, and 5) prediction of the next sound event in the sequence. The system's robustness is assessed with respect to complexity and noisiness of the signal. Clustering in isolation yields an adjusted Rand index (ARI) of 82.7% / 85.7% for data sets of singing voice and drums. Onset detection jointly with clustering achieve an ARI of 81.3% / 76.3% and the prediction of the entire system yields an ARI of 27.2% / 39.2%.