Regret Bounds and Regimes of Optimality for User-User and Item-Item Collaborative Filtering

We consider an online model for recommendation systems, with each user being recommended an item at each time-step and providing 'like' or 'dislike' feedback. Each user may be recommended a given item at most once. A latent variable model specifies the user preferences: both users and items are clustered into types. All users of a given type have identical preferences for the items, and similarly, items of a given type are either all liked or all disliked by a given user. We assume that the matrix encoding the preferences of each user type for each item type is randomly generated; in this way, the model captures structure in both the item and user spaces, the amount of structure depending on the number of each of the types. The measure of performance of the recommendation system is the expected number of disliked recommendations per user, defined as expected regret. We propose two algorithms inspired by user-user and item-item collaborative filtering (CF), modified to explicitly make exploratory recommendations, and prove performance guarantees in terms of their expected regret. For two regimes of model parameters, with structure only in item space or only in user space, we prove information-theoretic lower bounds on regret that match our upper bounds up to logarithmic factors. Our analysis elucidates system operating regimes in which existing CF algorithms are nearly optimal.Comment: 51 page

Achievability of Nonlinear Degrees of Freedom in Correlatively Changing Fading Channels

A new approach toward the noncoherent communications over the time varying fading channels is presented. In this approach, the relationship between the input signal space and the output signal space of a correlatively changing fading channel is shown to be a nonlinear mapping between manifolds of different dimensions. Studying this mapping, it is shown that using nonlinear decoding algorithms for single input-multiple output (SIMO) and multiple input multiple output (MIMO) systems, extra numbers of degrees of freedom (DOF) are available. We call them the nonlinear degrees of freedom

Communication Strategies for Low-Latency Trading

The possibility of latency arbitrage in financial markets has led to the deployment of high-speed communication links between distant financial centers. These links are noisy and so there is a need for coding. In this paper, we develop a gametheoretic model of trading behavior where two traders compete to capture latency arbitrage opportunities using binary signalling. Different coding schemes are strategies that trade off between reliability and latency. When one trader has a better channel, the second trader should not compete. With statistically identical channels, we find there are two different regimes of channel noise for which: there is a unique Nash equilibrium yielding ties; and there are two Nash equilibria with different winners.Comment: Will appear in IEEE International Symposium on Information Theory (ISIT), 201

Theoretical study of two prediction-centric problems : graphical model learning and recommendations

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 177-184).Motivated by prediction-centric learning problems, two problems are discussed in this thesis. PART I. Learning a tree-structured Ising model: We study the problem of learning a tree Ising model from samples such that subsequent predictions based on partial observations are accurate. Virtually all previous work on graphical model learning has focused on recovering the true underlying graph. We dene a distance ("small set TV" or ssTV) between distributions P and Q by taking the maximum, over all subsets S of a given size, of the total variation between the marginals of P and Q on S; this distance captures the accuracy of the prediction task of interest. We derive non-asymptotic bounds on the number of samples needed to get a distribution (from the same class) with small ssTV relative to the one generating the samples. An implication is that far fewer samples are needed for accurate predictions than for recovering the underlying tree. PART II. Optimal online algorithms for a latent variable model of recommendation systems: We consider an online model for recommendation systems, with each user being recommended an item at each time-step and providing 'like' or 'dislike' feedback. The user preferences are specified via a latent variable model: both users and items are clustered into types. The model captures structure in both the item and user spaces, and our focus is on simultaneous use of both structures. In the case when the type preference matrix is randomly generated, we provide a sharp analysis of the best possible regret obtainable by any algorithm.by Mina Karzand.Ph. D

Learning a tree-structured ising model in order to make predictions

We study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate. The prediction task considered in this paper is that of predicting the values of a subset of variables given values of some other subset of variables. Virtually all previous work on graphical model learning has focused on recovering the true underlying graph. We define a distance (“small set TV” or ssTV) between distributions P and Q by taking the maximum, over all subsets S of a given size, of the total variation between the marginals of P and Q on S; this distance captures the accuracy of the prediction task of interest. We derive nonasymptotic bounds on the number of samples needed to get a distribution (from the same class) with small ssTV relative to the one generating the samples. One of the main messages of this paper is that far fewer samples are needed than for recovering the underlying tree, which means that accurate predictions are possible using the wrong tree.United States. Office of Naval Research (Grant N00014-17-1-2147)United States. Defense Advanced Research Projects Agency (Grant W911NF-16-1-0551)National Science Foundation (U.S.). Computing and Communication Foundation (Grant CCF-1565516