We derive algorithms for generalised tensor factorisation (GTF) by building upon the well-established theory of Generalised Linear Models. Our algorithms are general in the sense that we can compute arbitrary factorisations in a message passing framework, derived for a broad class of exponential family distributions including special cases such as Tweedie's distributions corresponding to $\beta$-divergences. By bounding the step size of the Fisher Scoring iteration of the GLM, we obtain general updates for real data and multiplicative updates for non-negative data. The GTF framework is, then extended easily to address the problems when multiple observed tensors are factorised simultaneously. We illustrate our coupled factorisation approach on synthetic data as well as on a musical audio restoration problem.

How can we train a statistical mixture model on a massive data set? In this paper, we show how to construct coresets for mixtures of Gaussians and natural generalizations. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset will also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size independent of the size of the data set. More precisely, we prove that a weighted set of $O(dk^3/\eps^2)$ data points suffices for computing a $(1+\eps)$-approximation for the optimal model on the original $n$ data points. Moreover, such coresets can be efficiently constructed in a map-reduce style computation, as well as in a streaming setting. Our results rely on a novel reduction of statistical estimation to problems in computational geometry, as well as new complexity results about mixtures of Gaussians. We empirically evaluate our algorithms on several real data sets, including a density estimation problem in the context of earthquake detection using accelerometers in mobile phones.

The problem of multiclass boosting is considered. A new framework,based on multi-dimensional codewords and predictors is introduced. The optimal set of codewords is derived, and a margin enforcing loss proposed. The resulting risk is minimized by gradient descent on a multidimensional functional space. Two algorithms are proposed: 1) CD-MCBoost, based on coordinate descent, updates one predictor component at a time, 2) GD-MCBoost, based on gradient descent, updates all components jointly. The algorithms differ in the weak learners that they support but are both shown to be 1) Bayes consistent, 2) margin enforcing, and 3) convergent to the global minimum of the risk. They also reduce to AdaBoost when there are only two classes. Experiments show that both methods outperform previous multiclass boosting approaches on a number of datasets.

Extracting good representations from images is essential for many computer Vision tasks.

We introduce PiCoDes: a very compact image descriptor which nevertheless allows high performance on object category recognition. In particular, we address novel-category recognition: the task of defining indexing structures and image representations which enable a large collection of images to be searched for an object category that was not known when the index was built. Instead, the training images defining the category are supplied at query time. We explicitly learn descriptors of a given length (from as small as 16 bytes per image) which have good object-recognition performance. In contrast to previous work in the domain of object recognition, we do not choose an arbitrary intermediate representation, but explicitly learn short codes. In contrast to previous approaches to learn compact codes, we optimize explicitly for (an upper bound on) classification performance. Optimization directly for binary features is difficult and nonconvex, but we present an alternation scheme and convex upper bound which demonstrate excellent performance in practice. PiCoDes of 256 bytes match the accuracy of the current best known classifier for the Caltech256 benchmark, but they decrease the database storage size by a factor of 100 and speed-up the training and testing of novel classes by orders of magnitude.

Brain-computer interfaces (BCIs) use brain signals to convey a user's intent. Some BCI approaches begin by decoding kinematic parameters of movements from brain signals, and then proceed to using these signals, in absence of movements, to allow a user to control an output. Recent results have shown that electrocorticographic (ECoG)recordings from the surface of the brain in humans can give information about kinematic parameters (e.g., hand velocity or finger flexion). The decoding approaches in these demonstrations usually employed classical classification/regression algorithmsthat derive a linear mapping between brain signals and outputs. However, they typically only incorporate little prior information about the target kinematic parameter.

We introduce the Gamma-Exponential Process (GEP), a prior over a large family ofcontinuous time stochastic processes. A hierarchical version of this prior (HGEP; the Hierarchical GEP) yields a useful model for analyzing complex time series. Models based on HGEPs display many attractive properties: conjugacy, exchangeability and closed-form predictive distribution for the waiting times, and exact Gibbs updates for the time scale parameters. After establishing these properties, weshow how posterior inference can be carried efficiently using Particle MCMC methods [1]. This yields a MCMC algorithm that can resample entire sequences atomicallywhile avoiding the complications of introducing slice and stick auxiliary variables of the beam sampler [2]. We applied our model to the problem of estimating the disease progression in multiple sclerosis [3], and to RNA evolutionary modeling[4]. In both domains, we found that our model outperformed the standard rate matrix estimation approach.

Maximum entropy models have become popular statistical models in neuroscience and other areas in biology, and can be useful tools for obtaining estimates of mu- tual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling bias; i.e. the true entropy of the data can be severely underestimated. Here we study the sampling properties of estimates of the entropy obtained from maximum entropy models. We show that if the data is generated by a distribution that lies in the model class, the bias is equal to the number of parameters divided by twice the number of observations. However, in practice, the true distribution is usually outside the model class, and we show here that this misspecification can lead to much larger bias. We provide a perturba- tive approximation of the maximally expected bias when the true model is out of model class, and we illustrate our results using numerical simulations of an Ising model; i.e. the second-order maximum entropy distribution on binary data.

In the vast majority of recent work on sparse estimation algorithms, performance has been evaluated using ideal or quasi-ideal dictionaries (e.g., random Gaussian or Fourier) characterized by unit $\ell_2$ norm, incoherent columns or features. But in reality, these types of dictionaries represent only a subset of the dictionaries that are actually used in practice (largely restricted to idealized compressive sensing applications). In contrast, herein sparse estimation is considered in the context of structured dictionaries possibly exhibiting high coherence between arbitrary groups of columns and/or rows. Sparse penalized regression models are analyzed with the purpose of finding, to the extent possible, regimes of dictionary invariant performance. In particular, a Type II Bayesian estimator with a dictionary-dependent sparsity penalty is shown to have a number of desirable invariance properties leading to provable advantages over more conventional penalties such as the $\ell_1$ norm, especially in areas where existing theoretical recovery guarantees no longer hold. This can translate into improved performance in applications such as model selection with correlated features, source localization, and compressive sensing with constrained measurement directions.

We consider the problem of classification using similarity/distance functions over data. Specifically, we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose algorithms that have guaranteed generalization properties when working with such good functions. Our framework unifies and generalizes the frameworks proposed by (Balcan-Blum 2006) and (Wang et al 2007). An attractive feature of our framework is its adaptability to data - we do not promote a fixed notion of goodness but rather let data dictate it. We show, by giving theoretical guarantees that the goodness criterion best suited to a problem can itself be learned which makes our approach applicable to a variety of domains and problems. We propose a landmarking-based approach to obtaining a classifier from such learned goodness criteria. We then provide a novel diversity based heuristic to perform task-driven selection of landmark points instead of random selection. We demonstrate the effectiveness of our goodness criteria learning method as well as the landmark selection heuristic on a variety of similarity-based learning datasets and benchmark UCI datasets on which our method consistently outperforms existing approaches by a significant margin.