34 research outputs found
Ranking Median Regression: Learning to Order through Local Consensus
This article is devoted to the problem of predicting the value taken by a
random permutation , describing the preferences of an individual over a
set of numbered items say, based on the observation of
an input/explanatory r.v. e.g. characteristics of the individual), when
error is measured by the Kendall distance. In the probabilistic
formulation of the 'Learning to Order' problem we propose, which extends the
framework for statistical Kemeny ranking aggregation developped in
\citet{CKS17}, this boils down to recovering conditional Kemeny medians of
given from i.i.d. training examples . For this reason, this statistical learning problem is
referred to as \textit{ranking median regression} here. Our contribution is
twofold. We first propose a probabilistic theory of ranking median regression:
the set of optimal elements is characterized, the performance of empirical risk
minimizers is investigated in this context and situations where fast learning
rates can be achieved are also exhibited. Next we introduce the concept of
local consensus/median, in order to derive efficient methods for ranking median
regression. The major advantage of this local learning approach lies in its
close connection with the widely studied Kemeny aggregation problem. From an
algorithmic perspective, this permits to build predictive rules for ranking
median regression by implementing efficient techniques for (approximate) Kemeny
median computations at a local level in a tractable manner. In particular,
versions of -nearest neighbor and tree-based methods, tailored to ranking
median regression, are investigated. Accuracy of piecewise constant ranking
median regression rules is studied under a specific smoothness assumption for
's conditional distribution given
A connection between Tempering and Entropic Mirror Descent
This paper explores the connections between tempering (for Sequential Monte
Carlo; SMC) and entropic mirror descent to sample from a target probability
distribution whose unnormalized density is known.
We establish that tempering SMC is a numerical approximation of entropic
mirror descent applied to the Kullback-Leibler (KL) divergence and obtain
convergence rates for the tempering iterates.
Our result motivates the tempering iterates from an optimization point of
view, showing that tempering can be used as an alternative to Langevin-based
algorithms to minimize the KL divergence.
We exploit the connection between tempering and mirror descent iterates to
justify common practices in SMC and propose improvements to algorithms in
literature
Exponential Smoothing for Off-Policy Learning
Off-policy learning (OPL) aims at finding improved policies from logged
bandit data, often by minimizing the inverse propensity scoring (IPS) estimator
of the risk. In this work, we investigate a smooth regularization for IPS, for
which we derive a two-sided PAC-Bayes generalization bound. The bound is
tractable, scalable, interpretable and provides learning certificates. In
particular, it is also valid for standard IPS without making the assumption
that the importance weights are bounded. We demonstrate the relevance of our
approach and its favorable performance through a set of learning tasks. Since
our bound holds for standard IPS, we are able to provide insight into when
regularizing IPS is useful. Namely, we identify cases where regularization
might not be needed. This goes against the belief that, in practice, clipped
IPS often enjoys favorable performance than standard IPS in OPL.Comment: ICML 2023 (Oral and Poster
Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction
We address the problem of causal effect estima-tion in the presence of unobserved confounding,but where proxies for the latent confounder(s) areobserved. We propose two kernel-based meth-ods for nonlinear causal effect estimation in thissetting: (a) a two-stage regression approach, and(b) a maximum moment restriction approach. Wefocus on the proximal causal learning setting, butour methods can be used to solve a wider classof inverse problems characterised by a Fredholmintegral equation. In particular, we provide a uni-fying view of two-stage and moment restrictionapproaches for solving this problem in a nonlin-ear setting. We provide consistency guaranteesfor each algorithm, and demonstrate that these ap-proaches achieve competitive results on syntheticdata and data simulating a real-world task. In par-ticular, our approach outperforms earlier methodsthat are not suited to leveraging proxy variables
Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction
We address the problem of causal effect estimation in the presence of
unobserved confounding, but where proxies for the latent confounder(s) are
observed. We propose two kernel-based methods for nonlinear causal effect
estimation in this setting: (a) a two-stage regression approach, and (b) a
maximum moment restriction approach. We focus on the proximal causal learning
setting, but our methods can be used to solve a wider class of inverse problems
characterised by a Fredholm integral equation. In particular, we provide a
unifying view of two-stage and moment restriction approaches for solving this
problem in a nonlinear setting. We provide consistency guarantees for each
algorithm, and we demonstrate these approaches achieve competitive results on
synthetic data and data simulating a real-world task. In particular, our
approach outperforms earlier methods that are not suited to leveraging proxy
variables