We study consistency properties of surrogate loss functions for general multiclass classification problems, defined by a general loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be classification calibrated with respect to a loss matrix in this setting. We then introduce the notion of \emph{classification calibration dimension} of a multiclass loss matrix, which measures the smallest `size' of a prediction space for which it is possible to design a convex surrogate that is classification calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, as one application, we provide a different route from the recent result of Duchi et al.\ (2010) for analyzing the difficulty of designing `low-dimensional' convex surrogates that are consistent with respect to pairwise subset ranking losses. We anticipate the classification calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.

Robust policy optimization acknowledges that risk-aversion plays a vital role in real-world decision-making. When faced with uncertainty about the effects of actions, the policy that maximizes expected utility over the unknown parameters of the system may also carry with it a risk of intolerably poor performance. One might prefer to accept lower utility in expectation in order to avoid, or reduce the likelihood of, unacceptable levels of utility under harmful parameter realizations. In this paper, we take a Bayesian approach to parameter uncertainty, but unlike other methods avoid making any distributional assumptions about the form of this uncertainty. Instead we focus on identifying optimization objectives for which solutions can be efficiently approximated. We introduce percentile measures: a very general class of objectives for robust policy optimization, which encompasses most existing approaches, including ones known to be intractable. We then introduce a broad subclass of this family for which robust policies can be approximated efficiently. Finally, we frame these objectives in the context of a two-player, zero-sum, extensive-form game and employ a no-regret algorithm to approximate an optimal policy, with computation only polynomial in the number of states and actions of the MDP.

Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data.

Discrete mixtures are used routinely in broad sweeping applications ranging from unsupervised settings to fully supervised multi-task learning. Indeed, finite mixtures and infinite mixtures, relying on Dirichlet processes and modifications, have become a standard tool. One important issue that arises in using discrete mixtures is low separation in the components; in particular, different components can be introduced that are very similar and hence redundant. Such redundancy leads to too many clusters that are too similar, degrading performance in unsupervised learning and leading to computational problems and an unnecessarily complex model in supervised settings. Redundancy can arise in the absence of a penalty on components placed close together even when a Bayesian approach is used to learn the number of components. To solve this problem, we propose a novel prior that generates components from a repulsive process, automatically penalizing redundant components. We characterize this repulsive prior theoretically and propose a Markov chain Monte Carlo sampling algorithm for posterior computation. The methods are illustrated using synthetic examples and an iris data set.

A key function of brains is undoubtedly the abstraction and maintenance of information from the environment for later use. Neurons in association cortex play an important role in this process: during learning these neurons become tuned to relevant features and represent the information that is required later as a persistent elevation of their activity. It is however not well known how these neurons acquire their task-relevant tuning. Here we introduce a biologically plausible learning scheme that explains how neurons become selective for relevant information when animals learn by trial and error. We propose that the action selection stage feeds back attentional signals to earlier processing levels. These feedback signals interact with feedforward signals to form synaptic tags at those connections that are responsible for the stimulus-response mapping. A globally released neuromodulatory signal interacts with these tagged synapses to determine the sign and strength of plasticity. The learning scheme is generic because it can train networks in different tasks, simply by varying inputs and rewards. It explains how neurons in association cortex learn to (1) temporarily store task-relevant information in non-linear stimulus-response mapping tasks and (2) learn to optimally integrate probabilistic evidence for perceptual decision making.

The National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) database contains a large amount of information, regarding the way of life, medical conditions, depression, etc., of a representative sample of the U.S. population. In the present paper, we are interested in seeking the hidden causes behind the suicide attempts, for which we propose to model the subjects using a nonparametric latent model based on the Indian Buffet Process (IBP). Due to the nature of the data, we need to adapt the observation model for discrete random variables. We propose a generative model in which the observations are drawn from a multinomial-logit distribution given the IBP matrix. The implementation of an efficient Gibbs sampler is accomplished using the Laplace approximation, which allows us to integrate out the weighting factors of the multinomial-logit likelihood model. Finally, the experiments over the NESARC database show that our model properly captures some of the hidden causes that model suicide attempts.

Neural adaptation underlies the ability of neurons to maximize encoded information over a wide dynamic range of input stimuli. While adaptation is an intrinsic feature of neuronal models like the Hodgkin-Huxley model, the challenge is to integrate adaptation in models of neural computation. Recent computational models like the Adaptive Spike Response Model implement adaptation as spike-based addition of fixed-size fast spike-triggered threshold dynamics and slow spike-triggered currents. Such adaptation has been shown to accurately model neural spiking behavior over a limited dynamic range. Taking a cue from kinetic models of adaptation, we propose a multiplicative Adaptive Spike Response Model where the spike-triggered adaptation dynamics are scaled multiplicatively by the adaptation state at the time of spiking. We show that unlike the additive adaptation model, the firing rate in the multiplicative adaptation model saturates to a maximum spike-rate. When simulating variance switching experiments, the model also quantitatively fits the experimental data over a wide dynamic range. Furthermore, dynamic threshold models of adaptation suggest a straightforward interpretation of neural activity in terms of dynamic signal encoding with shifted and weighted exponential kernels. We show that when thus encoding rectified filtered stimulus signals, the multiplicative Adaptive Spike Response Model achieves a high coding efficiency and maintains this efficiency over changes in the dynamic signal range of several orders of magnitude, without changing model parameters.

We present a novel method for learning densities with bounded support which enables us to incorporate `hard' topological constraints. In particular, we show how emerging techniques from computational algebraic topology and the notion of Persistent Homology can be combined with kernel based methods from Machine Learning for the purpose of density estimation. The proposed formalism facilitates learning of models with bounded support in a principled way, and -- by incorporating Persistent Homology techniques in our approach -- we are able to encode algebraic-topological constraints which are not addressed in current state-of the art probabilistic models. We study the behaviour of our method on two synthetic examples for various sample sizes and exemplify the benefits of the proposed approach on a real-world data-set by learning a motion model for a racecar. We show how to learn a model which respects the underlying topological structure of the racetrack, constraining the trajectories of the car.

The paper addresses the problem of generating multiple hypotheses for prediction tasks that involve interaction with users or successive components in a cascade. Given a set of multiple hypotheses, such components/users have the ability to automatically rank the results and thus retrieve the best one. The standard approach for handling this scenario is to learn a single model and then produce M-best Maximum a Posteriori (MAP) hypotheses from this model. In contrast, we formulate this multiple {\em choice} learning task as a multiple-output structured-output prediction problem with a loss function that captures the natural setup of the problem. We present a max-margin formulation that minimizes an upper-bound on this loss-function. Experimental results on the problems of image co-segmentation and protein side-chain prediction show that our method outperforms conventional approaches used for this scenario and leads to substantial improvements in prediction accuracy.

We offer a regularized, kernel extension of the multi-set, orthogonal Procrustes problem, or hyperalignment. Our new method, called Kernel Hyperalignment, expands the scope of hyperalignment to include nonlinear measures of similarity and enables the alignment of multiple datasets with a large number of base features. With direct application to fMRI data analysis, kernel hyperalignment is well-suited for multi-subject alignment of large ROIs, including the entire cortex. We conducted experiments using real-world, multi-subject fMRI data.