Patch-based methods have been widely used for noise reduction in recent years. In this paper, we propose a general statistical aggregation method which combines image patches denoised with several commonly-used algorithms. We show that weakly denoised versions of the input image obtained with standard methods, can serve to compute an efficient patch-based aggregated estimator. In our approach, we evaluate the Stein's Unbiased Risk Estimator (SURE) of each denoised candidate imagepatch and use this information to compute the exponential weighted aggregation (EWA) estimator. The aggregation method is flexible enough to combine anystandard denoising algorithm and has an interpretation with Gibbs distribution. Thedenoising algorithm (PEWA) is based on a MCMC sampling and is able to produce results that are comparable to the current state-of-the-art.

We present a theoretical analysis of F-measures for binary, multiclass and multilabel classification. These performance measures are non-linear, but in many scenarios they are pseudo-linear functions of the per-class false negative/false positive rate. Based on this observation, we present a general reduction of F-measure maximization to cost-sensitive classification with unknown costs. We then propose an algorithm with provable guarantees to obtain an approximately optimal classifier for the F-measure by solving a series of cost-sensitive classification problems. The strength of our analysis is to be valid on any dataset and any class of classifiers, extending the existing theoretical results on F-measures, which are asymptotic in nature. We present numerical experiments to illustrate the relative importance of cost asymmetry and thresholding when learning linear classifiers on various F-measure optimization tasks.

Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process. The model infers the location of the next VB optimum from a sequence of noisy realizations. As a consequence of this construction, we update the variational parameters using Bayes rule, rather than a hand-crafted optimization schedule. When our model is a Kalman filter this procedure can recover the original SVI algorithm and SVI with adaptive steps. We may also encode additional assumptions in the model, such as heavy-tailed noise. By doing so, our algorithm outperforms the original SVI schedule and a state-of-the-art adaptive SVI algorithm in two diverse domains.

It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encodingof such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions usinga spike based spatiotemporal code. Our model combines the computational advantagesof the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, themodel highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative populationlevel approachesfor the experimental validation of distributed representations. Core brain computations, such as sensory perception, have been successfully characterized as probabilistic inference,whereby sensory stimuli are interpreted in terms of the objects or features that gave rise to them [1, 2].

We propose modeling time series by representing the transformations that take a frame at time t to a frame at time t+1. To this end we show how a bi-linear model of transformations, such as a gated autoencoder, can be turned into a recurrent network, by training it to predict future frames from the current one and the inferred transformation using backprop-through-time. We also show how stacking multiple layers of gating units in a recurrent pyramid makes it possible to represent the ”syntax” of complicated time series, and that it can outperform standard recurrent neural networks in terms of prediction accuracy on a variety of tasks.

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.

This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these models which guarantees the global consistency of distributed estimators, provided the local estimators are consistent.

Partial monitoring is a general model for online learning with limited feedback: a learner chooses actions in a sequential manner while an opponent chooses outcomes. In every round, the learner suffers some loss and receives some feedback based on the action and the outcome. The goal of the learner is to minimize her cumulative loss. Applications range from dynamic pricing to label-efficient prediction to dueling bandits. In this paper, we assume that we are given some prior information about the distribution based on which the opponent generates the outcomes. We propose BPM, a family of new efficient algorithms whose core is to track the outcome distribution with an ellipsoid centered around the estimated distribution. We show that our algorithm provably enjoys near-optimal regret rate for locally observable partial-monitoring problems against stochastic opponents. As demonstrated with experiments on synthetic as well as real-world data, the algorithm outperforms previous approaches, even for very uninformed priors, with an order of magnitude smaller regret and lower running time.

The accurate estimation of covariance matrices is essential for many signal processing and machine learning algorithms. In high dimensional settings the sample covariance is known to perform poorly, hence regularization strategies such as analytic shrinkage of Ledoit/Wolf are applied. In the standard setting, i.i.d. data is assumed, however, in practice, time series typically exhibit strong autocorrelation structure, which introduces a pronounced estimation bias. Recent work by Sancetta has extended the shrinkage framework beyond i.i.d. data. We contribute in this work by showing that the Sancetta estimator, while being consistent in the high-dimensional limit, suffers from a high bias in finite sample sizes. We propose an alternative estimator, which is (1) unbiased, (2) less sensitive to hyperparameter choice and (3) yields superior performance in simulations on toy data and on a real world data set from an EEG-based Brain-Computer-Interfacing experiment.

We address the problem of image collection summarization by learning mixtures of submodular functions. We argue that submodularity is very natural to this problem, and we show that a number of previously used scoring functions are submodular — a property not explicitly mentioned in these publications. We provide classes of submodular functions capturing the necessary properties of summaries, namely coverage, likelihood, and diversity. To learn mixtures of these submodular functions as scoring functions, we formulate summarization as a supervised learning problem using large-margin structured prediction. Furthermore, we introduce a novel evaluation metric, which we call V-ROUGE, for automatic summary scoring. While a similar metric called ROUGE has been successfully applied to document summarization [14], no such metric was known for quantifying the quality of image collection summaries. We provide a new dataset consisting of 14 real-world image collections along with many human-generated ground truth summaries collected using mechanical turk. We also extensively compare our method with previously explored methods for this problem and show that our learning approach outperforms all competitors on this new dataset. This paper provides, to our knowledge, the first systematic approach for quantifying the problem of image collection summarization, along with a new dataset of image collections and human summaries.