Probabilistic Models over Ordered Partitions with Application in Learning to Rank

This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial state space with unknown numbers of partitions and unknown ordering among them. We approach the problem from the discrete choice theory, where subsets are chosen in a stagewise manner, reducing the state space per each stage significantly. Further, we show that with suitable parameterisation, we can still learn the models in linear time. We evaluate the proposed models on the problem of learning to rank with the data from the recently held Yahoo! challenge, and demonstrate that the models are competitive against well-known rivals.Comment: 19 pages, 2 figure

Just Sort It! A Simple and Effective Approach to Active Preference Learning

We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking, the optimal solution is to use an efficient sorting algorithm, such as Quicksort. But how do sorting algorithms behave if some comparison outcomes are inconsistent with the ranking? We give favorable guarantees for Quicksort for the popular Bradley-Terry model, under natural assumptions on the parameters. Furthermore, we empirically demonstrate that sorting algorithms lead to a very simple and effective active learning strategy: repeatedly sort the items. This strategy performs as well as state-of-the-art methods (and much better than random sampling) at a minuscule fraction of the computational cost.Comment: Accepted at ICML 201

Behavioural decisions & welfare

If decision-makers (DMs) do not always do what is in their best interest, what do choices reveal about welfare? This paper shows how observed choices can reveal whether the DM is acting in her own best interest. We study a framework that relaxes rationality in a way that is common across a variety of seemingly disconnected positive behavioral models and admits the standard rational choice model as a special case. We model a behavioral DM (boundedly rational) who, in contrast to a standard DM (rational), does not fully internalize all the consequences of her own actions on herself. We provide an axiomatic characterization of choice correspondences consistent with behavioral and standard DMs, propose a choice experiment to infer the divergence between choice and welfare, state an existence result for incomplete preferences and show that the choices of behavioral DMs are, typically, sub-optimal

Characterizing behavioral decisions with choice data

This paper provides an axiomatic characterization of choices in a setting where a decision-maker may not fully internalize all the consequences of her choices on herself. Such a departure from rationality, it turns out, is common across a variety of positive behavioral models and admits the standard rational choice model as a special case. We show that choice data satisfying (a) Senís axioms if and fully characterize behavioral decisions, and (b) Senís axiom if and if fully characterize standard decision-making. In addition, we show that (a) it is possible to identify a minimal and a maximal set of psychological states using choice data alone, and (b) under specific choice scenarios, "revealed mistakes" can be inferred directly from choice data

Behavioural Decisions and Welfare

What are the normative implications of behavioral economics? We study a model where the decisions a person makes, consciously or unconsciously, affect her psychological state (reference point, beliefs, expectations, self-image) which, in turn, impacts on her ranking over available decisions in the first place. We distinguish between standard decisions where the decision-maker internalizes the feedback from her actions to her psychological state, and behavioural decisions where the psychological state is taken as given (although a decision outcome requires that action and psychological state are mutually consistent). In a behavioural decision, the individual imposes an externality on herself. We provide an axiomatic characterization of behavioral decisions. We show that the testable implications of behavioral and standard decisions are different and the outcomes of the two decision problems are, typically, distinguishable. We discuss the consequences for public policy of our formal analysis and over normative grounds for subsidized psychological therapiesBehavioural Decisions; Indistinguishabilty; revealed preferences; normative preferences; welfare; paternalism; autonomy; existence