Neural Information Processing Systems http://nips.cc/

Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time

Cross-V alidation (CV) is the default choice for estimate the out-of-sample performance of machine learning models.

Variational inference algorithms provide the most effective framework for large-scale training of Bayesian nonparametric models. Stochastic online approaches are promising, but are sensitive to the chosen learning rate and often converge to poor local optima. We present a new algorithm, memoized online variational inference, which scales to very large (yet finite) datasets while avoiding the complexities of stochastic gradient. Our algorithm maintains finite-dimensional sufficient statistics from batches of the full dataset, requiring some additional memory but still scaling to millions of examples. Exploiting nested families of variational bounds for infinite nonparametric models, we develop principled birth and merge moves allowing non-local optimization.

We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti representation theorem and the construction of random distribution functions made by Ferguson (1973). This approach allows for flexible uncertainty modeling in both the latent score and the mapping to probabilities. We demonstrate the method performance using simulated data where it outperforms standard logistic regression.

Parametric Bayesian modeling offers a powerful and flexible toolbox for scientific data analysis. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we study nonparametrically perturbed parametric (NPP) Bayesian models, in which a parametric Bayesian model is relaxed via a distortion of its likelihood. We analyze the properties of NPP models when the target of inference is the true data distribution or some functional of it, such as in causal inference. We show that NPP models can offer the robustness of nonparametric models while retaining the data efficiency of parametric models, achieving fast convergence when the parametric model is close to true. To efficiently analyze data with an NPP model, we develop a generalized Bayes procedure to approximate its posterior. We demonstrate our method by estimating causal effects of gene expression from single cell RNA sequencing data. NPP modeling offers an efficient approach to robust Bayesian inference and can be used to robustify any parametric Bayesian model.

Applications of Bayesian nonparametric methods require learning and inference algorithms which efficiently explore models of unbounded complexity. We develop new Markov chain Monte Carlo methods for the beta process hidden Markov model (BP-HMM), enabling discovery of shared activity patterns in large video and motion capture databases. By introducing split-merge moves based on sequential allocation, we allow large global changes in the shared feature structure. We also develop data-driven reversible jump moves which more reliably discover rare or unique behaviors. Our proposals apply to any choice of conjugate likelihood for observed data, and we show success with multinomial, Gaussian, and autoregressive emission models. Together, these innovations allow tractable analysis of hundreds of time series, where previous inference required clever initialization and lengthy burn-in periods for just six sequences.

We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs sampler for posterior simulation. We develop a time-varying extension of our model, and apply it to the New York Times lists of weekly bestselling books.