arXiv research

Neural networks approximate random utility models for choice prediction.

Improved semialgebraic choices with linear complexity.

Choice models, which capture popular preferences over objects of interest, play a key role in making decisions whose eventual outcome is impacted by human choice behavior. In most scenarios, the choice model, which can effectively be viewed as a distribution over permutations, must be learned from observed data. The ob…

Optimizes choice sets to influence group decisions.

The study explores various localized bases and their duals for scattered data approximation.

Develops a new model for collateral choice options under stochastic rates.

DMNL bandits optimize assortment choices balancing relevance and diversity.

Many applications in preference learning assume that decisions come from the maximization of a stable utility function. Yet a large experimental literature shows that individual choices and judgements can be affected by "irrelevant" aspects of the context in which they are made. An important class of such contexts is t…

Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact inference is often intractable. Markov chain Monte Carlo techniques make approximat…

We introduce Neural Choice by Elimination, a new framework that integrates deep neural networks into probabilistic sequential choice models for learning to rank. Given a set of items to chose from, the elimination strategy starts with the whole item set and iteratively eliminates the least worthy item in the remaining …

Improved likelihood-free inference by localizing and refining low-dimensional approximations.

Possibilistic risk theory starts from the hypothesis that risk is modelled by fuzzy numbers. In particular, in a possibilistic portfolio choice problem, the return of a risky asset will be a fuzzy number. The expected utility operators have been introduced in a previous paper to build an abstract theory of possibilisti…

New method approximates curvature from symmetries in deep networks.

Specifying utility functions is a key step towards applying the discrete choice framework for understanding the behaviour processes that govern user choices. However, identifying the utility function specifications that best model and explain the observed choices can be a very challenging and time-consuming task. This …

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. We propose a novel…

This paper tackles scalability issues in kernel logistic regression for large datasets.

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in \mathbb N$ of possible point evaluations $f(x_i)$, $i=1,...,m$, of $f$, which we …

In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex functions. The proposed framework is based on a nontrivial combination of the majorizatio…

Active learning method for ABC statistics selection reduces expert work and improves posterior estimates.

KrigHedge uses Gaussian processes to approximate option Greeks efficiently.

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the var…

New method quantifies uncertainty in fine-tuned LLMs using LoRA ensembles.

Variational inference methods often focus on the problem of efficient model optimization, with little emphasis on the choice of the approximating posterior. In this paper, we review and implement the various methods that enable us to develop a rich family of approximating posteriors. We show that one particular method …

Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that constructs an approximation to the true likelihood based on the similarity between …

Bayesian neural networks' performance varies with prior choice, affecting their ability to identify unknowns.

This manuscript shows that AdaBoost and its immediate variants can produce approximate maximum margin classifiers simply by scaling step size choices with a fixed small constant. In this way, when the unscaled step size is an optimal choice, these results provide guarantees for Friedman's empirically successful "shrink…

New algorithm for computing Wasserstein barycenters with guarantees.

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true when the model is well-specified, which is often not the case in practice. In thi…

We investigate a class of binary choice models with social interactions. We propose a unifying perspective that integrates economic models using a utility function and psychological models using an impact function. A general approach for analyzing the equilibrium structure of these models within mean-field approximatio…

Bayesian DL model improves DCMs for better predictive and inferential performance.

Assortment optimization is an important problem that arises in many industries such as retailing and online advertising where the goal is to find a subset of products from a universe of substitutable products which maximize seller's expected revenue. One of the key challenges in this problem is to model the customer su…

A new model uses neural networks for consistent discrete choice analysis.

The paper proposes using function approximations to reduce the computational burden in measuring counterparty credit exposure.

New framework improves variational inference for high-dimensional posteriors.

NVGD uses neural networks to infer distributions without kernel choices.

Kristensen and Mele (2011) developed a new approach to obtain closed-form approximations to continuous-time derivatives pricing models. The approach uses a power series expansion of the pricing bias between an intractable model and some known auxiliary model. Since the resulting approximation formula has closed-form it…

Rational neural networks approximate functions more efficiently with less depth.

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization prob…

New algorithm tackles dynamic assortment optimization with knapsack constraints.

Transformers can approximate posterior predictive distributions through in-context learning.

We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared between the workers. We approximate the model evidence for the full data set through…

Unified view of GP approximations improves efficiency.

One of the core problems in variational inference is a choice of approximate posterior distribution. It is crucial to trade-off between efficient inference with simple families as mean-field models and accuracy of inference. We propose a variant of a greedy approximation of the posterior distribution with tractable bas…

Method uses NMF for clustering with partial distance measurements.

Amortized inference allows latent-variable models trained via variational learning to scale to large datasets. The quality of approximate inference is determined by two factors: a) the capacity of the variational distribution to match the true posterior and b) the ability of the recognition network to produce good vari…

We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences.…

Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep Set learning. This work investigates a core component of Deep Set architecture: ag…

The paper studies how regularization parameters affect sparsity in deep neural networks.