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.

The primary application of collaborate filtering (CF) is to recommend a small set of items to a user, which entails ranking. Most approaches, however, formulate the CF problem as rating prediction, overlooking the ranking perspective. In this work we present a method for collaborative ranking that leverages the strengths of the two main CF approaches, neighborhood- and model-based. Our novel method is highly efficient, with only seventeen parameters to optimize and a single hyperparameter to tune, and beats the state-of-the-art collaborative ranking methods. We also show that parameters learned on one dataset yield excellent results on a very different dataset, without any retraining.

Modelling natural images with sparse coding (SC) has faced two main challenges: flexibly representing varying pixel intensities and realistically representing lowlevel imagecomponents. This paper proposes a novel multiple-cause generative model of low-level image statistics that generalizes the standard SC model in two crucial points: (1) it uses a spike-and-slab prior distribution for a more realistic representation of component absence/intensity, and (2) the model uses the highly nonlinear combination rule of maximal causes analysis (MCA) instead of a linear combination.The major challenge is parameter optimization because a model with either (1) or (2) results in strongly multimodal posteriors. We show for the first time that a model combining both improvements can be trained efficiently while retaining the rich structure of the posteriors. We design an exact piecewise Gibbssampling method and combine this with a variational method based on preselection of latent dimensions. This combined training scheme tackles both analytical and computational intractability and enables application of the model to a large number of observed and hidden dimensions. Applying the model to image patches we study the optimal encoding of images by simple cells in V1 and compare the model's predictions with in vivo neural recordings.

This paper introduces a novel classification method for functional magnetic resonance imaging datasets with tens of classes. The method is designed to make predictions using information from as many brain locations as possible, instead of resorting to feature selection, and does this by decomposing the pattern of brain activation into differently informative sub-regions. We provide results over a complex semantic processing dataset that show that the method is competitive with state-of-the-art feature selection and also suggest how the method may be used to perform group or exploratory analyses of complex class structure.

We develop a scalable algorithm for posterior inference of overlapping communities in large networks. Our algorithm is based on stochastic variational inference in the mixed-membership stochastic blockmodel. It naturally interleaves subsampling the network with estimating its community structure. We apply our algorithm on ten large, real-world networks with up to 60,000 nodes. It converges several orders of magnitude faster than the state-of-the-art algorithm for MMSB, finds hundreds of communities in large real-world networks, and detects the true communities in 280 benchmark networks with equal or better accuracy compared to other scalable algorithms.

In the conventional approaches for supervised parametric learning, relations between data and target variables are provided through training sets consisting of pairs of corresponded data and target variables. In this work, we describe a new learning scheme for parametric learning, in which the target variables $\y$ can be modeled with a prior model $p(\y)$ and the relations between data and target variables are estimated through $p(\y)$ and a set of uncorresponded data $\x$ in training. We term this method as learning with target priors (LTP). Specifically, LTP learning seeks parameter $\t$ that maximizes the log likelihood of $f_\t(\x)$ on a uncorresponded training set with regards to $p(\y)$. Compared to the conventional (semi)supervised learning approach, LTP can make efficient use of prior knowledge of the target variables in the form of probabilistic distributions, and thus removes/reduces the reliance on training data in learning. Compared to the Bayesian approach, the learned parametric regressor in LTP can be more efficiently implemented and deployed in tasks where running efficiency is critical, such as on-line BCI signal decoding. We demonstrate the effectiveness of the proposed approach on parametric regression tasks for BCI signal decoding and pose estimation from video.

We propose a Deep Boltzmann Machine for learning a generative model of multimodal data. We show how to use the model to extract a meaningful representation of multimodal data. We find that the learned representation is useful for classification and information retreival tasks, and hence conforms to some notion of semantic similarity. The model defines a probability density over the space of multimodal inputs. By sampling from the conditional distributions over each data modality, it possible to create the representation even when some data modalities are missing. Our experimental results on bi-modal data consisting of images and text show that the Multimodal DBM can learn a good generative model of the joint space of image and text inputs that is useful for information retrieval from both unimodal and multimodal queries. We further demonstrate that our model can significantly outperform SVMs and LDA on discriminative tasks. Finally, we compare our model to other deep learning methods, including autoencoders and deep belief networks, and show that it achieves significant gains.

Hashing is a common method to reduce large, potentially infinite feature vectors to a fixed-size table. In reinforcement learning, hashing is often used in conjunction withtile coding to represent states in continuous spaces. Hashing is also a promising approach to value function approximation in large discrete domains such as Go and Hearts, where feature vectors can be constructed by exhaustively combining a set of atomic features. Unfortunately, the typical use of hashing in value function approximation results in biased value estimates due to the possibility ofcollisions. Recent work in data stream summaries has led to the development of the tug-of-war sketch, an unbiased estimator for approximating inner products. Our work investigates the application of this new data structure to linear value function approximation. Although in the reinforcement learning setting the use of the tug-of-war sketch leads to biased value estimates, we show that this bias can be orders of magnitude less than that of standard hashing. We provide empirical results on two RL benchmark domains and fifty-five Atari 2600 games to highlight the superior learning performance obtained when using tug-of-war hashing.

We develop a new algorithm to cluster sparse unweighted graphs -- i.e. partition the nodes into disjoint clusters so that there is higher density within clusters, and low across clusters. By sparsity we mean the setting where both the in-cluster and across cluster edge densities are very small, possibly vanishing in the size of the graph. Sparsity makes the problem noisier, and hence more difficult to solve. Any clustering involves a tradeoff between minimizing two kinds of errors: missing edges within clusters and present edges across clusters. Our insight is that in the sparse case, these must be {\em penalized differently}. We analyze our algorithm's performance on the natural, classical and widely studied ``planted partition'' model (also called the stochastic block model); we show that our algorithm can cluster sparser graphs, and with smaller clusters, than all previous methods. This is seen empirically as well.

Many tasks in text and speech processing and computational biology require estimating functionsmapping strings to real numbers. A broad class of such functions can be defined by weighted automata. Spectral methods based on the singular valuedecomposition of a Hankel matrix have been recently proposed for learning a probability distribution represented by a weighted automaton from a training sample drawn according to this same target distribution. In this paper, we show how spectral methods can be extended to the problem of learning a general weighted automaton from a sample generated by an arbitrary distribution. The main obstruction to this approach is that, in general, some entries of the Hankel matrix may be missing. We present a solution to this problem based on solving a constrained matrix completion problem. Combining these two ingredients, matrix completion and spectral method, a whole new family of algorithms for learning general weighted automata is obtained.