Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

Chérief-Abdellatif, Badr-Eddine; Alquier, Pierre

doi:10.48550/arxiv.1912.05737

Cited by 4 publications

(13 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, in all our preliminary simulations, the choice of k Y as a Gaussian kernel lead to mild results. Note that this is in accordance with the simulations in [12,13] where the exponential kernel leads to much better results in the case of the estimation of the mean of a Gaussian variable. However, for other kernels, there is no explicit formula for the MMD distance.…”

Section: Gaussian Regressionsupporting

confidence: 91%

“…where the first inequality holds by ( [16], Proposition E.5). Together, (11) and (12) show that the sequence ( fn ) n≥1 is indeed Cauchy w.r.t. the • H(k S ) norm, and the proof of the lemma is complete.…”

Section: Proof Of Theoremmentioning

confidence: 88%

“…This is not adapted to practical regression scenarios, where one wants to estimate the distribution Y |X, but not the distribution of X. The main novelty in this paper is to extend the MMD method of [4,12] to the regression setting, as well as the consistency analysis. This step turns out to be nontrivial, especially in the random design case.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Universal Robust Regression via Maximum Mean Discrepancy

Alquier¹,

Gerber²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Many datasets are collected automatically, and are thus easily contaminated by outliers. In order to overcome this issue, there was recently a regain of interest in robust estimation methods. However, most of these methods are designed for a specific purpose, such as estimation of the mean, or linear regression. We propose estimators based on Maximum Mean Discrepancy (MMD) optimization as a universal framework for robust regression. We provide non-asymptotic error bounds, and show that our estimators are robust to Huber-type contamination. We discuss the optimization of the objective functions via (stochastic) gradient descent in classical examples such as linear, logistic or Poisson regression. These results are illustrated by a set of simulations.

show abstract

Section: Gaussian Regressionsupporting

confidence: 91%

Section: Proof Of Theoremmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Universal Robust Regression via Maximum Mean Discrepancy

Alquier¹,

Gerber²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The MMD also leads to robust estimators; i.e. estimators which will return reasonable estimates even in the presence of outliers in the data or mild model misspecification [25], [26]. The median heuristic is a reasonable choice for balancing robustness and efficiency as discussed in [25].…”

Section: Discussionmentioning

confidence: 99%

“…These moments are then used for calibration in an ABC framework, where we use the maximum mean discrepancy (MMD) [24] to compare the distribution of simulated and measured data. The MMD has previously been used for frequentist inference in [25], [26], and in a Bayesian sense in [27]. Specific ABC methods using kernels include [28]- [31], and the MMD has also been used to train generative adversarial networks in [32]- [34].…”

Section: Introductionmentioning

confidence: 99%

A General Method for Calibrating Stochastic Radio Channel Models with Kernels

Bharti¹,

Briol²,

Pedersen³

2020

Preprint

View full text Add to dashboard Cite

Calibrating stochastic radio channel models to new measurement data is challenging when the likelihood function is intractable. The standard approach to this problem involves sophisticated algorithms for extraction and clustering of multipath components, following which, point estimates of the model parameters can be obtained using specialized estimators. We propose a likelihood-free calibration method using approximate Bayesian computation. The method is based on the maximum mean discrepancy, which is a notion of distance between probability distributions. Our method not only by-passes the need to implement any high-resolution or clustering algorithm, but is also automatic in that it does not require any additional input or manual pre-processing from the user. It also has the advantage of returning an entire posterior distribution on the value of the parameters, rather than a simple point estimate. We evaluate the performance of the proposed method by fitting two different stochastic channel models, namely the Saleh-Valenzuela model and the propagation graph model, to both simulated and measured data. The proposed method is able to estimate the parameters of both the models accurately in simulations, as well as when applied to 60 GHz indoor measurement data.

show abstract

Estimation of copulas via Maximum Mean Discrepancy

Alquier,

Chérief-Abdellatif,

Derumigny

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

This paper deals with robust inference for parametric copula models. Estimation using Canonical Maximum Likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the Maximum Mean Discrepancy (MMD) principle. We derive non-asymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on [0, 1] d , as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available.

show abstract

Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

Cited by 4 publications

References 40 publications

Universal Robust Regression via Maximum Mean Discrepancy

Universal Robust Regression via Maximum Mean Discrepancy

A General Method for Calibrating Stochastic Radio Channel Models with Kernels

Estimation of copulas via Maximum Mean Discrepancy

Contact Info

Product

Resources

About