Inferring key unobservable features of individuals is an important task in the applied sciences. In particular, an important source of data in fields such as marketing, social sciences and medicine is questionnaires: answers in such questionnaires are noisy measures of target unobserved features. While comprehensive surveys help to better estimate the latent variables of interest, aiming at a high number of questions comes at a price: refusal to participate in surveys can go up, as well as the rate of missing data; quality of answers can decline; costs associated with applying such questionnaires can also increase. In this paper, we cast the problem of refining existing models for questionnaire data as follows: solve a constrained optimization problem of preserving the maximum amount of information found in a latent variable model using only a subset of existing questions. The goal is to find an optimal subset of a given size. For that, we first define an information theoretical measure for quantifying the quality of a reduced questionnaire. Three different approximate inference methods are introduced to solve this problem. Comparisons against a simple but powerful heuristic are presented.

This paper introduces two new frameworks for learning action models for planning. In the mistake-bounded planning framework, the learner has access to a planner for the given model representation, a simulator, and a planning problem generator, and aims to learn a model with at most a polynomial number of faulty plans. In the planned exploration framework, the learner does not have access to a problem generator and must instead design its own problems, plan for them, and converge with at most a polynomial number of planning attempts. The paper reduces learning in these frameworks to concept learning with one-sided error and provides algorithms for successful learning in both frameworks. A specific family of hypothesis spaces is shown to be efficiently learnable in both the frameworks.

Knowledge-based support vector machines (KBSVMs) incorporate advice from domain experts, which can improve generalization significantly. A major limitation that has not been fully addressed occurs when the expert advice is imperfect, which can lead to poorer models. We propose a model that extends KBSVMs and is able to not only learn from data and advice, but also simultaneously improve the advice. The proposed approach is particularly effective for knowledge discovery in domains with few labeled examples. The proposed model contains bilinear constraints, and is solved using two iterative approaches: successive linear programming and a constrained concave-convex approach. Experimental results demonstrate that these algorithms yield useful refinements to expert advice, as well as improve the performance of the learning algorithm overall.

Computational analyses of dendritic computations often assume stationary inputs to neurons, ignoring the pulsatile nature of spike-based communication between neurons and the moment-to-moment fluctuations caused by such spiking inputs. Conversely, circuit computations with spiking neurons are usually formalized without regard to the rich nonlinear nature of dendritic processing. Here we address the computational challenge faced by neurons that compute and represent analogue quantities but communicate with digital spikes, and show that reliable computation of even purely linear functions of inputs can require the interplay of strongly nonlinear subunits within the postsynaptic dendritic tree. Our theory predicts a matching of dendritic nonlinearities and synaptic weight distributions to the joint statistics of presynaptic inputs. This approach suggests normative roles for some puzzling forms of nonlinear dendritic dynamics and plasticity.

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations. Our main target in this paper is dense type regularizations including ℓp-MKL that imposes ℓp-mixed-norm regularization instead of ℓ1-mixed-norm regularization. According to the recent numerical experiments, the sparse regularization does not necessarily show a good performance compared with dense type regularizations. Motivated by this fact, this paper gives a general theoretical tool to derive fast learning rates that is applicable to arbitrary monotone norm-type regularizations in a unifying manner. As a by-product of our general result, we show a fast learning rate of ℓp-MKL that is tightest among existing bounds. We also show that our general learning rate achieves the minimax lower bound. Finally, we show that, when the complexities of candidate reproducing kernel Hilbert spaces are inhomogeneous, dense type regularization shows better learning rate compared with sparse ℓ1 regularization.

Consider a sequence of bits where we are trying to predict the next bit from the previous bits. Assume we are allowed to say `predict 0' or `predict 1', and our payoff is $+1$ if the prediction is correct and $-1$ otherwise. We will say that at each point in time the loss of an algorithm is the number of wrong predictions minus the number of right predictions so far. In this paper we are interested in algorithms that have essentially zero (expected) loss over any string at any point in time and yet have small regret with respect to always predicting $0$ or always predicting $1$. For a sequence of length $T$ our algorithm has regret $14\epsilon T $ and loss $2\sqrt{T}e^{-\epsilon^2 T} $ in expectation for all strings. We show that the tradeoff between loss and regret is optimal up to constant factors. Our techniques extend to the general setting of $N$ experts, where the related problem of trading off regret to the best expert for regret to the 'special' expert has been studied by Even-Dar et al. (COLT'07). We obtain essentially zero loss with respect to the special expert and optimal loss/regret tradeoff, improving upon the results of Even-Dar et al (COLT'07) and settling the main question left open in their paper. The strong loss bounds of the algorithm have some surprising consequences. First, we obtain a parameter free algorithm for the experts problem that has optimal regret bounds with respect to $k$-shifting optima, i.e. bounds with respect to the optimum that is allowed to change arms multiple times. Moreover, for {\em any window of size $n$} the regret of our algorithm to any expert never exceeds $O(\sqrt{n(\log N+\log T)})$, where $N$ is the number of experts and $T$ is the time horizon, while maintaining the essentially zero loss property.

In this paper we consider general rank minimization problems with rank appearing ineither objective function or constraint. We first show that a class of matrix optimization problems can be solved as lower dimensional vector optimization problems. As a consequence, we establish that a class of rank minimization problems haveclosed form solutions. Using this result, we then propose penalty decomposition methodsfor general rank minimization problems. The convergence results of the PD methods have been shown in the longer version of the paper [19]. Finally, we test the performance of our methods by applying them to matrix completion and nearest low-rank correlation matrix problems. The computational results demonstrate that our methods generally outperform the existing methods in terms of solution quality and/or speed.

Neurons typically respond to a restricted number of stimulus features within the high-dimensional space of natural stimuli. Here we describe an explicit model-based interpretation of traditional estimators for a neuron's multi-dimensional feature space, which allows for several important generalizations and extensions. First, we show that traditional estimators based on the spike-triggered average (STA) and spike-triggered covariance (STC) can be formalized in terms of the "expected log-likelihood" of a Linear-Nonlinear-Poisson (LNP) model with Gaussian stimuli. This model-based formulation allows us to define maximum-likelihood and Bayesian estimators that are statistically consistent and efficient in a wider variety of settings, such as with naturalistic (non-Gaussian) stimuli. It also allows us to employ Bayesian methods for regularization, smoothing, sparsification, and model comparison, and provides Bayesian confidence intervals on model parameters. We describe an empirical Bayes method for selecting the number of features, and extend the model to accommodate an arbitrary elliptical nonlinear response function, which results in a more powerful and more flexible model for feature space inference. We validate these methods using neural data recorded extracellularly from macaque primary visual cortex.

Diagnosis of Alzheimer's disease (AD) at the early stage of the disease development is of great clinical importance. Current clinical assessment that relies primarily on cognitive measures proves low sensitivity and specificity. The fast growing neuroimaging techniques hold great promise. Research so far has focused on single neuroimaging modalities. However, as different modalities provide complementary measures for the same disease pathology, fusion of multi-modality data may increase the statistical power in identification of disease-related brain regions. This is especially true for early AD, at which stage the disease-related regions are most likely to be weak-effect regions that are difficult to be detected from a single modality alone. We propose a sparse composite linear discriminant analysis model (SCLDA) for identification of disease-related brain regions of early AD from multi-modality data. SCLDA uses a novel formulation that decomposes each LDA parameter into a product of a common parameter shared by all the modalities and a parameter specific to each modality, which enables joint analysis of all the modalities and borrowing strength from one another. We prove that this formulation is equivalent to a penalized likelihood with non-convex regularization, which can be solved by the DC ((difference of convex functions) programming. We show that in using the DC programming, the property of the non-convex regularization in terms of preserving weak-effect features can be nicely revealed. We perform extensive simulations to show that SCLDA outperforms existing competing algorithms on feature selection, especially on the ability for identifying weak-effect features. We apply SCLDA to the Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) images of 49 AD patients and 67 normal controls (NC). Our study identifies disease-related brain regions consistent with findings in the AD literature.

The multi-armed bandit (MAB) setting is a useful abstraction of many online learning tasks which focuses on the trade-off between exploration and exploitation. In this setting, an online algorithm has a fixed set of alternatives ("arms"), and in each round it selects one arm and then observes the corresponding reward. While the case of small number of arms is by now well-understood, a lot of recent work has focused on multi-armed bandits with (infinitely) many arms, where one needs to assume extra structure in order to make the problem tractable. In particular, in the Lipschitz MAB problem there is an underlying similarity metric space, known to the algorithm, such that any two arms that are close in this metric space have similar payoffs. In this paper we consider the more realistic scenario in which the metric space is *implicit* -- it is defined by the available structure but not revealed to the algorithm directly. Specifically, we assume that an algorithm is given a tree-based classification of arms. For any given problem instance such a classification implicitly defines a similarity metric space, but the numerical similarity information is not available to the algorithm. We provide an algorithm for this setting, whose performance guarantees (almost) match the best known guarantees for the corresponding instance of the Lipschitz MAB problem.