3,217 research outputs found
Conformalization of Sparse Generalized Linear Models
Given a sequence of observable variables , the conformal prediction method estimates a confidence set for
given that is valid for any finite sample size by merely
assuming that the joint distribution of the data is permutation invariant.
Although attractive, computing such a set is computationally infeasible in most
regression problems. Indeed, in these cases, the unknown variable can
take an infinite number of possible candidate values, and generating conformal
sets requires retraining a predictive model for each candidate. In this paper,
we focus on a sparse linear model with only a subset of variables for
prediction and use numerical continuation techniques to approximate the
solution path efficiently. The critical property we exploit is that the set of
selected variables is invariant under a small perturbation of the input data.
Therefore, it is sufficient to enumerate and refit the model only at the change
points of the set of active features and smoothly interpolate the rest of the
solution via a Predictor-Corrector mechanism. We show how our path-following
algorithm accurately approximates conformal prediction sets and illustrate its
performance using synthetic and real data examples.Comment: ICML 202
Predicting Skin Permeability by means of Computational Approaches : Reliability and Caveats in Pharmaceutical Studies
© 2019 American Chemical Society.The skin is the main barrier between the internal body environment and the external one. The characteristics of this barrier and its properties are able to modify and affect drug delivery and chemical toxicity parameters. Therefore, it is not surprising that permeability of many different compounds has been measured through several in vitro and in vivo techniques. Moreover, many different in silico approaches have been used to identify the correlation between the structure of the permeants and their permeability, to reproduce the skin behavior, and to predict the ability of specific chemicals to permeate this barrier. A significant number of issues, like interlaboratory variability, experimental conditions, data set building rationales, and skin site of origin and hydration, still prevent us from obtaining a definitive predictive skin permeability model. This review wants to show the main advances and the principal approaches in computational methods used to predict this property, to enlighten the main issues that have arisen, and to address the challenges to develop in future research.Peer reviewedFinal Accepted Versio
Root-finding Approaches for Computing Conformal Prediction Set
Conformal prediction constructs a confidence set for an unobserved response
of a feature vector based on previous identically distributed and exchangeable
observations of responses and features. It has a coverage guarantee at any
nominal level without additional assumptions on their distribution. Its
computation deplorably requires a refitting procedure for all replacement
candidates of the target response. In regression settings, this corresponds to
an infinite number of model fit. Apart from relatively simple estimators that
can be written as pieces of linear function of the response, efficiently
computing such sets is difficult and is still considered as an open problem. We
exploit the fact that, \emph{often}, conformal prediction sets are intervals
whose boundaries can be efficiently approximated by classical root-finding
algorithm. We investigate how this approach can overcome many limitations of
formerly used strategies and we discuss its complexity and drawbacks
Bayesian Optimization with Conformal Prediction Sets
Bayesian optimization is a coherent, ubiquitous approach to decision-making
under uncertainty, with applications including multi-arm bandits, active
learning, and black-box optimization. Bayesian optimization selects decisions
(i.e. objective function queries) with maximal expected utility with respect to
the posterior distribution of a Bayesian model, which quantifies reducible,
epistemic uncertainty about query outcomes. In practice, subjectively
implausible outcomes can occur regularly for two reasons: 1) model
misspecification and 2) covariate shift. Conformal prediction is an uncertainty
quantification method with coverage guarantees even for misspecified models and
a simple mechanism to correct for covariate shift. We propose conformal
Bayesian optimization, which directs queries towards regions of search space
where the model predictions have guaranteed validity, and investigate its
behavior on a suite of black-box optimization tasks and tabular ranking tasks.
In many cases we find that query coverage can be significantly improved without
harming sample-efficiency.Comment: For code, see
https://www.github.com/samuelstanton/conformal-bayesopt.gi
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