When data and the associated topics are indexed by time dimension, it is of interest to study the temporal dynamics of such latent geometric structures.

We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ( n p 1). In this regime, optimization algorithms can immensely benefit from approximate second order information. We propose an alternative way of constructing the curvature information by formulating it as an estimation problem and applying a Stein-type lemma, which allows further improvements through sub-sampling and eigenvalue thresh-olding. Our algorithm enjoys fast convergence rates, resembling that of second order methods, with modest per-iteration cost. We provide its convergence analysis for the case where the rows of the design matrix are i.i.d.

In this paper, we study the following online sampling problem: Problem 1.1.

We introduce the Gaussian Process Convolution Model (GPCM), a two-stage nonparametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise process and a continuous-time linear filter drawn from Gaussian process. The GPCM is a continuous-time nonparametric-window moving average process and, conditionally, is itself a Gaussian process with a nonparametric kernel defined in a probabilistic fashion. The generative model can be equivalently considered in the frequency domain, where the power spectral density of the signal is specified using a Gaussian process. One of the main contributions of the paper is to develop a novel variational free-energy approach based on inter-domain inducing variables that efficiently learns the continuous-time linear filter and infers the driving white-noise process. In turn, this scheme provides closed-form probabilistic estimates of the covariance kernel and the noise-free signal both in denoising and prediction scenarios. Additionally, the variational inference procedure provides closed-form expressions for the approximate posterior of the spectral density given the observed data, leading to new Bayesian nonparametric approaches to spectrum estimation. The proposed GPCM is validated using synthetic and real-world signals.

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

Matrix factorization (MF) collaborative filtering is an effective and widely used method in recommendation systems. However, the problem of finding an optimal trade-off between exploration and exploitation (otherwise known as the bandit problem), a crucial problem in collaborative filtering from cold-start, has not been previously addressed. In this paper, we present a novel algorithm for online MF recommendation that automatically combines finding the most relevant items with exploring new or less-recommended items. Our approach, called Particle Thompson sampling for MF (PTS), is based on the general Thompson sampling framework, but augmented with a novel efficient online Bayesian probabilistic matrix factorization method based on the Rao-Blackwellized particle filter. Extensive experiments in collaborative filtering using several real-world datasets demonstrate that PTS significantly outperforms the current state-of-the-arts.

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

We describe a novel method for training high-quality image denoising models based on unorganized collections of corrupted images. The training does not need access to clean reference images, or explicit pairs of corrupted images, and can thus be applied in situations where such data is unacceptably expensive or impossible to acquire. We build on a recent technique that removes the need for reference data by employing networks with a "blind spot" in the receptive field, and significantly improve two key aspects: image quality and training efficiency. Our result quality is on par with state-of-the-art neural network denoisers in the case of i.i.d.