In many large economic markets, goods are sold through sequential auctions. Such domains include eBay, online ad auctions, wireless spectrum auctions, and the Dutch flower auctions. Bidders in these domains face highly complex decision-making problems, as their preferences for outcomes in one auction often depend on the outcomes of other auctions, and bidders have limited information about factors that drive outcomes, such as other bidders' preferences and past actions. In this work, we formulate the bidder's problem as one of price prediction (i.e., learning) and optimization. We define the concept of stable price predictions and show that (approximate) equilibrium in sequential auctions can be characterized as a profile of strategies that (approximately) optimize with respect to such (approximately) stable price predictions. We show how equilibria found with our formulation compare to known theoretical equilibria for simpler auction domains, and we find new approximate equilibria for a more complex auction domain where analytical solutions were heretofore unknown.

In many applications, one has information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks nearby that pre-specified target region. Locally-biased problems of this sort are particularly challenging for popular eigenvector-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities. In this paper, we address this issue by providing a methodology to construct semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these locally-biased eigenvectors can be used to perform locally-biased machine learning. These semi-supervised eigenvectors capture successively-orthogonalized directions of maximum variance, conditioned on being well-correlated with an input seed set of nodes that is assumed to be provided in a semi-supervised manner. We also provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning.

The question of aggregating pairwise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR’s TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining ranking, finding ‘scores’ for each object (e.g. player’s rating) is of interest to understanding the intensity of the preferences. In this paper, we propose a novel iterative rank aggregation algorithm for discovering scores for objects from pairwise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with edges present between two objects if they are compared; the scores turn out to be the stationary probability of this random walk. The algorithm is model independent. To establish the efficacy of our method, however, we consider the popular Bradley-Terry-Luce (BTL) model in which each object has an associated score which determines the probabilistic outcomes of pairwise comparisons between objects. We bound the finite sample error rates between the scores assumed by the BTL model and those estimated by our algorithm. This, in essence, leads to order-optimal dependence on the number of samples required to learn the scores well by our algorithm. Indeed, the experimental evaluation shows that our (model independent) algorithm performs as well as the Maximum Likelihood Estimator of the BTL model and outperforms a recently proposed algorithm by Ammar and Shah [1].

Sparse learning models typically combine a smooth loss with a nonsmooth penalty, such as trace norm. Although recent developments in sparse approximation have offered promising solution methods, current approaches either apply only to matrix-norm constrained problems or provide suboptimal convergence rates. In this paper, we propose a boosting method for regularized learning that guarantees $\epsilon$ accuracy within $O(1/\epsilon)$ iterations. Performance is further accelerated by interlacing boosting with fixed-rank local optimization---exploiting a simpler local objective than previous work. The proposed method yields state-of-the-art performance on large-scale problems. We also demonstrate an application to latent multiview learning for which we provide the first efficient weak-oracle.

Parametric policy search algorithms are one of the methods of choice for the optimisation of Markov Decision Processes, with Expectation Maximisation and natural gradient ascent being considered the current state of the art in the field. In this article we provide a unifying perspective of these two algorithms by showing that their step-directions in the parameter space are closely related to the search direction of an approximate Newton method. This analysis leads naturally to the consideration of this approximate Newton method as an alternative gradient-based method for Markov Decision Processes. We are able show that the algorithm has numerous desirable properties, absent in the naive application of Newton's method, that make it a viable alternative to either Expectation Maximisation or natural gradient ascent. Empirical results suggest that the algorithm has excellent convergence and robustness properties, performing strongly in comparison to both Expectation Maximisation and natural gradient ascent.

We consider the estimation of an i.i.d.\ vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise (possibly nonlinear) measurement channel. We present a method, called adaptive generalized approximate message passing (Adaptive GAMP), that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector $\xbf$. The proposed algorithm is a generalization of a recently-developed method by Vila and Schniter that uses expectation-maximization (EM) iterations where the posteriors in the E-steps are computed via approximate message passing. The techniques can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear-nonlinear cascade models in dynamical systems and neural spiking processes. We prove that for large i.i.d.\ Gaussian transform matrices the asymptotic componentwise behavior of the adaptive GAMP algorithm is predicted by a simple set of scalar state evolution equations. This analysis shows that the adaptive GAMP method can yield asymptotically consistent parameter estimates, which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values. The adaptive GAMP methodology thus provides a systematic, general and computationally efficient method applicable to a large range of complex linear-nonlinear models with provable guarantees.

A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is natural to formulate structured sparsity inducing priors using submodular functions, and we use their Lovász extension to obtain a convex relaxation. For tractable classes such as Gaussian graphical models, this leads to a convex optimization problem that can be efficiently solved. We show that our method results in an improvement in the accuracy of reconstructed networks for synthetic data. We also show how our prior encourages scale-free reconstructions on a bioinfomatics dataset.

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.

Conditional Markov Chains (also known as Linear-Chain Conditional Random Fields in the literature) are a versatile class of discriminative models for the distribution of a sequence of hidden states conditional on a sequence of observable variables. Large-sample properties of Conditional Markov Chains have been first studied by Sinn and Poupart [1]. The paper extends this work in two directions: first, mixing properties of models with unbounded feature functions are being established; second, necessary conditions for model identifiability and the uniqueness of maximum likelihood estimates are being given.

We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward and backward sweeps as in PG-BS, however, we achieve the same effect in a single forward sweep. We apply the PG-AS framework to the challenging class of non-Markovian state-space models. We develop a truncation strategy of these models that is applicable in principle to any backward-simulation-based method, but which is particularly well suited to the PG-AS framework. In particular, as we show in a simulation study, PG-AS can yield an order-of-magnitude improved accuracy relative to PG-BS due to its robustness to the truncation error. Several application examples are discussed, including Rao-Blackwellized particle smoothing and inference in degenerate state-space models.