Learning Economic Parameters from Revealed Preferences

A recent line of work, starting with Beigman and Vohra (2006) and Zadimoghaddam and Roth (2012), has addressed the problem of {\em learning} a utility function from revealed preference data. The goal here is to make use of past data describing the purchases of a utility maximizing agent when faced with certain prices and budget constraints in order to produce a hypothesis function that can accurately forecast the {\em future} behavior of the agent. In this work we advance this line of work by providing sample complexity guarantees and efficient algorithms for a number of important classes. By drawing a connection to recent advances in multi-class learning, we provide a computationally efficient algorithm with tight sample complexity guarantees ($\Theta(d/\epsilon)$ for the case of $d$ goods) for learning linear utility functions under a linear price model. This solves an open question in Zadimoghaddam and Roth (2012). Our technique yields numerous generalizations including the ability to learn other well-studied classes of utility functions, to deal with a misspecified model, and with non-linear prices

Image-based Recommendations on Styles and Substitutes

Humans inevitably develop a sense of the relationships between objects, some of which are based on their appearance. Some pairs of objects might be seen as being alternatives to each other (such as two pairs of jeans), while others may be seen as being complementary (such as a pair of jeans and a matching shirt). This information guides many of the choices that people make, from buying clothes to their interactions with each other. We seek here to model this human sense of the relationships between objects based on their appearance. Our approach is not based on fine-grained modeling of user annotations but rather on capturing the largest dataset possible and developing a scalable method for uncovering human notions of the visual relationships within. We cast this as a network inference problem defined on graphs of related images, and provide a large-scale dataset for the training and evaluation of the same. The system we develop is capable of recommending which clothes and accessories will go well together (and which will not), amongst a host of other applications.Comment: 11 pages, 10 figures, SIGIR 201

Social welfare and profit maximization from revealed preferences

Consider the seller's problem of finding optimal prices for her $n$ (divisible) goods when faced with a set of $m$ consumers, given that she can only observe their purchased bundles at posted prices, i.e., revealed preferences. We study both social welfare and profit maximization with revealed preferences. Although social welfare maximization is a seemingly non-convex optimization problem in prices, we show that (i) it can be reduced to a dual convex optimization problem in prices, and (ii) the revealed preferences can be interpreted as supergradients of the concave conjugate of valuation, with which subgradients of the dual function can be computed. We thereby obtain a simple subgradient-based algorithm for strongly concave valuations and convex cost, with query complexity $O(m^2/\epsilon^2)$, where $\epsilon$ is the additive difference between the social welfare induced by our algorithm and the optimum social welfare. We also study social welfare maximization under the online setting, specifically the random permutation model, where consumers arrive one-by-one in a random order. For the case where consumer valuations can be arbitrary continuous functions, we propose a price posting mechanism that achieves an expected social welfare up to an additive factor of $O(\sqrt{mn})$ from the maximum social welfare. Finally, for profit maximization (which may be non-convex in simple cases), we give nearly matching upper and lower bounds on the query complexity for separable valuations and cost (i.e., each good can be treated independently)

Vertical string-pulling in green jays (Cyanocorax yncas)

The cognition of green jays (Cyanocorax yncas), a non Corvus corvid species, was investigated by using the string-pulling paradigm. Five adult green jays performed a vertical string-pulling task in which they had to retrieve a worm attached to the end of a vertical hanging string while sitting on their perch. In the first experiment, three of the subjects managed to retrieve the worm by pulling on the string with their beaks and stepping on the resulting loop, and thereafter repeating this sequence until the worm was accessible. When subjects were given a choice between two strings in subsequent experiments 2–4, they chose at random between the string connected to the worm and the one connected to a slice of a wooden dowel. In experiment 5, subjects that had failed the previous discrimination series were able, nevertheless, to solve a more stringent vertical string array in which they had to pull up the whole length of the string without any visual access to the worm at the end. We discuss green jays’ performance in comparison with other corvid species in which cognition has been more extensively investigated

Complexity of Strong Implementability

We consider the question of implementability of a social choice function in a classical setting where the preferences of finitely many selfish individuals with private information have to be aggregated towards a social choice. This is one of the central questions in mechanism design. If the concept of weak implementation is considered, the Revelation Principle states that one can restrict attention to truthful implementations and direct revelation mechanisms, which implies that implementability of a social choice function is easy to check. For the concept of strong implementation, however, the Revelation Principle becomes invalid, and the complexity of deciding whether a given social choice function is strongly implementable has been open so far. In this paper, we show by using methods from polyhedral theory that strong implementability of a social choice function can be decided in polynomial space and that each of the payments needed for strong implementation can always be chosen to be of polynomial encoding length. Moreover, we show that strong implementability of a social choice function involving only a single selfish individual can be decided in polynomial time via linear programming

Inferring Networks of Substitutable and Complementary Products

In a modern recommender system, it is important to understand how products relate to each other. For example, while a user is looking for mobile phones, it might make sense to recommend other phones, but once they buy a phone, we might instead want to recommend batteries, cases, or chargers. These two types of recommendations are referred to as substitutes and complements: substitutes are products that can be purchased instead of each other, while complements are products that can be purchased in addition to each other. Here we develop a method to infer networks of substitutable and complementary products. We formulate this as a supervised link prediction task, where we learn the semantics of substitutes and complements from data associated with products. The primary source of data we use is the text of product reviews, though our method also makes use of features such as ratings, specifications, prices, and brands. Methodologically, we build topic models that are trained to automatically discover topics from text that are successful at predicting and explaining such relationships. Experimentally, we evaluate our system on the Amazon product catalog, a large dataset consisting of 9 million products, 237 million links, and 144 million reviews.Comment: 12 pages, 6 figure

Gaze following in ungulates: Domesticated and non-domesticated species follow the gaze of both human and conspecifics in an experimental context

Gaze following is the ability to use others’ gaze to obtain information about the environment (e.g., food location, predators, and social interactions). As such, it may be highly adaptive in a variety of socio-ecological contexts, and thus be widespread across animal taxa. To date, gaze following has been mostly studied in primates, and partially in birds, but little is known on the gaze following abilities of other taxa and, especially, on the evolutionary pressures that led to their emergence. In this study, we used an experimental approach to test gaze following skills in a still understudied taxon, ungulates. Across four species (i.e., domestic goats and lamas, and non-domestic guanacos and mouflons), we assessed the individual ability to spontaneously follow the gaze of both conspecifics and human experimenters in different conditions. In line with our predictions, species followed the model’s gaze both with human and conspecific models, but more likely with the latter. Except for guanacos, all species showed gaze following significantly more in the experimental conditions (than in the control ones). Despite the relative low number of study subjects, our study provides the first experimental evidence of gaze following skills in non-domesticated ungulates, and contributes to understanding how gaze following skills are distributed in another taxon—an essential endeavor to identify the evolutionary pressures leading to the emergence of gaze following skills across taxa

Statistical mechanics of systems with heterogeneous agents: Minority Games

We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytic findings.Comment: 4 pages, 1 Postscript figure. Revised versio

The Governance and Performance of Research Universities: Evidence from Europe and the U.S.

We investigate how university governance affects research output, measured by patenting and international university research rankings. For both European and U.S. universities, we generate several measures of autonomy, governance, and competition for research funding. We show that university autonomy and competition are positively correlated with university output, both among European countries and among U.S. public universities. We then identity a (political) source of exogenous shocks to funding of U.S. universities. We demonstrate that, when a state's universities receive a positive funding shock, they produce more patents if they are more autonomous and face more competition from private research universities. Finally, we show that during periods when merit-based competitions for federal research funding have been most prominent, universities produce more patents when they receive an exogenous funding shock, suggesting that routine participation in such competitions hones research skill.