arXiv subjects

Vincent Lemaire

Publications and source records attributed to Vincent Lemaire.

At least 55 records · Page 3Linked to original sources

arXiv2021

Importance Reweighting for Biquality Learning

The field of Weakly Supervised Learning (WSL) has recently seen a surge of popularity, with numerous papers addressing different types of "supervision deficiencies", namely: poor quality, non adaptability, and insufficient quantity of labels. Regarding quality, label noise can be of different types, including completely-at-random, at-random or even not-at-random. All these kinds of label noise are addressed separately in the literature, leading to highly specialized approaches. This paper proposes an original, encompassing, view of Weakly Supervised Learning, which results in the design of generic approaches capable of dealing with any kind of label noise. For this purpose, an alternative setting called "Biquality data" is used. It assumes that a small trusted dataset of correctly labeled examples is available, in addition to an untrusted dataset of noisy examples. In this paper, we propose a new reweigthing scheme capable of identifying noncorrupted examples in the untrusted dataset. This allows one to learn classifiers using both datasets. Extensive experiments that simulate several types of label noise and that vary the quality and quantity of untrusted examples, demonstrate that the proposed approach outperforms baselines and state-of-the-art approaches.

cs.LG↗

arXiv2021

Contrastive Representations for Label Noise Require Fine-Tuning

In this paper we show that the combination of a Contrastive representation with a label noise-robust classification head requires fine-tuning the representation in order to achieve state-of-the-art performances. Since fine-tuned representations are shown to outperform frozen ones, one can conclude that noise-robust classification heads are indeed able to promote meaningful representations if provided with a suitable starting point. Experiments are conducted to draw a comprehensive picture of performances by featuring six methods and nine noise instances of three different kinds (none, symmetric, and asymmetric). In presence of noise the experiments show that fine tuning of Contrastive representation allows the six methods to achieve better results than end-to-end learning and represent a new reference compare to the recent state of art. Results are also remarkable stable versus the noise level.

cs.LG↗

arXiv2021

On the intrinsic robustness to noise of some leading classifiers and symmetric loss function -- an empirical evaluation

In some industrial applications such as fraud detection, the performance of common supervision techniques may be affected by the poor quality of the available labels : in actual operational use-cases, these labels may be weak in quantity, quality or trustworthiness. We propose a benchmark to evaluate the natural robustness of different algorithms taken from various paradigms on artificially corrupted datasets, with a focus on noisy labels. This paper studies the intrinsic robustness of some leading classifiers. The algorithms under scrutiny include SVM, logistic regression, random forests, XGBoost, Khiops. Furthermore, building on results from recent literature, the study is supplemented with an investigation into the opportunity to enhance some algorithms with symmetric loss functions.

cs.LG↗

arXiv2021

Early Classification of Time Series is Meaningful

Many approaches have been proposed for early classification of time series in light of its significance in a wide range of applications including healthcare, transportation and finance. However, recently a preprint saved on Arxiv claim that all research done for almost 20 years now on the Early Classification of Time Series is useless, or, at the very least, ill-oriented because severely lacking a strong ground. In this paper, we answer in detail the main issues and misunderstandings raised by the authors of the preprint, and propose directions to further expand the fields of application of early classification of time series.

cs.LG↗

arXiv2021

From Weakly Supervised Learning to Biquality Learning: an Introduction

The field of Weakly Supervised Learning (WSL) has recently seen a surge of popularity, with numerous papers addressing different types of "supervision deficiencies". In WSL use cases, a variety of situations exists where the collected "information" is imperfect. The paradigm of WSL attempts to list and cover these problems with associated solutions. In this paper, we review the research progress on WSL with the aim to make it as a brief introduction to this field. We present the three axis of WSL cube and an overview of most of all the elements of their facets. We propose three measurable quantities that acts as coordinates in the previously defined cube namely: Quality, Adaptability and Quantity of information. Thus we suggest that Biquality Learning framework can be defined as a plan of the WSL cube and propose to re-discover previously unrelated patches in WSL literature as a unified Biquality Learning literature.

cs.LG↗

arXiv2021

Interpretable Feature Construction for Time Series Extrinsic Regression

Supervised learning of time series data has been extensively studied for the case of a categorical target variable. In some application domains, e.g., energy, environment and health monitoring, it occurs that the target variable is numerical and the problem is known as time series extrinsic regression (TSER). In the literature, some well-known time series classifiers have been extended for TSER problems. As first benchmarking studies have focused on predictive performance, very little attention has been given to interpretability. To fill this gap, in this paper, we suggest an extension of a Bayesian method for robust and interpretable feature construction and selection in the context of TSER. Our approach exploits a relational way to tackle with TSER: (i), we build various and simple representations of the time series which are stored in a relational data scheme, then, (ii), a propositionalisation technique (based on classical aggregation / selection functions from the relational data field) is applied to build interpretable features from secondary tables to "flatten" the data; and (iii), the constructed features are filtered out through a Bayesian Maximum A Posteriori approach. The resulting transformed data can be processed with various existing regressors. Experimental validation on various benchmark data sets demonstrates the benefits of the suggested approach.

cs.LG↗

arXiv2020

Learning active learning at the crossroads? evaluation and discussion

Active learning aims to reduce annotation cost by predicting which samples are useful for a human expert to label. Although this field is quite old, several important challenges to using active learning in real-world settings still remain unsolved. In particular, most selection strategies are hand-designed, and it has become clear that there is no best active learning strategy that consistently outperforms all others in all applications. This has motivated research into meta-learning algorithms for "learning how to actively learn". In this paper, we compare this kind of approach with the association of a Random Forest with the margin sampling strategy, reported in recent comparative studies as a very competitive heuristic. To this end, we present the results of a benchmark performed on 20 datasets that compares a strategy learned using a recent meta-learning algorithm with margin sampling. We also present some lessons learned and open future perspectives.

cs.LG↗

arXiv2020

Predictive K-means with local models

Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no guarantee that they are useful for labels prediction. Predictive clustering seeks to obtain the best of the two worlds. Starting from labeled data, it looks for clusters that are as pure as possible with regards to the class labels. One technique consists in tweaking a clustering algorithm so that data points sharing the same label tend to aggregate together. With distance-based algorithms, such as k-means, a solution is to modify the distance used by the algorithm so that it incorporates information about the labels of the data points. In this paper, we propose another method which relies on a change of representation guided by class densities and then carries out clustering in this new representation space. We present two new algorithms using this technique and show on a variety of data sets that they are competitive for prediction performance with pure supervised classifiers while offering interpretability of the clusters discovered.

cs.LG↗

arXiv2020

Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization

A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the deterministic initial condition of the volatility by its invariant measure and show, based on calibrated parameters, that this model produce a steeper smile for short maturities than the Standard Heston model. We also present numerical solution based on Product Recursive Quantization for the evaluation of exotic options (Bermudan and Barrier options).

q-fin.MF↗

arXiv2020

New Weak Error bounds and expansions for Optimal Quantization

We propose new weak error bounds and expansion in dimension one for optimal quantization-based cubature formula for different classes of functions, such that piecewise affine functions, Lipschitz convex functions or differentiable function with piecewise-defined locally Lipschitz or $α$-Hölder derivatives. This new results rest on the local behaviors of optimal quantizers, the $L^r$-$L^s$ distribution mismatch problem and Zador's Theorem. This new expansion supports the definition of a Richardson-Romberg extrapolation yielding a better rate of convergence for the cubature formula. An extension of this expansion is then proposed in higher dimension for the first time. We then propose a novel variance reduction method for Monte Carlo estimators, based on one dimensional optimal quantizers.

math.PR↗

arXiv2020

Quantization-based Bermudan option pricing in the $FX$ world

This paper proposes two numerical solution based on Product Optimal Quantization for the pricing of Foreign Echange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we consider a 3-factor model. For these two numerical methods, we give an estimation of the $L^2$-error induced by such approximations and we illustrate them with market-based examples that highlight the speed of such methods.

q-fin.CP↗

arXiv2019

Should we Reload Time Series Classification Performance Evaluation ? (a position paper)

Since the introduction and the public availability of the \textsc{ucr} time series benchmark data sets, numerous Time Series Classification (TSC) methods has been designed, evaluated and compared to each others. We suggest a critical view of TSC performance evaluation protocols put in place in recent TSC literature. The main goal of this `position' paper is to stimulate discussion and reflexion about performance evaluation in TSC literature.

stat.ML↗

arXiv2018

Thinning and Multilevel Monte Carlo for Piecewise Deterministic (Markov) Processes. Application to a stochastic Morris-Lecar model

In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak error expansion for Piecewise Deterministic Markov Processes (PDMP). These estimates are the building blocks of the Multilevel Monte Carlo (MLMC) method which we study in the second part. The coupling required by MLMC is based on the thinning procedure. In the third part we apply these results to a 2-dimensional Morris-Lecar model with stochastic ion channels. In the range of our simulations the MLMC estimator outperforms the classical Monte Carlo one.

math.PR↗

arXiv2018

Day-ahead time series forecasting: application to capacity planning

In the context of capacity planning, forecasting the evolution of informatics servers usage enables companies to better manage their computational resources. We address this problem by collecting key indicator time series and propose to forecast their evolution a day-ahead. Our method assumes that data is structured by a daily seasonality, but also that there is typical evolution of indicators within a day. Then, it uses the combination of a clustering algorithm and Markov Models to produce day-ahead forecasts. Our experiments on real datasets show that the data satisfies our assumption and that, in the case study, our method outperforms classical approaches (AR, Holt-Winters).

cs.AI↗

arXiv2018

Weak error for nested Multilevel Monte Carlo

This article discusses MLMC estimators with and without weights, applied to nested expectations of the form E [f (E [F (Y, Z)|Y ])]. More precisely, we are interested on the assumptions needed to comply with the MLMC framework, depending on whether the payoff function f is smooth or not. A new result to our knowledge is given when f is not smooth in the development of the weak error at an order higher than 1, which is needed for a successful use of MLMC estimators with weights.

math.PR↗

arXiv2017

Exact simulation of the jump times of a class of Piecewise Deterministic Markov Processes

In this paper, we are interested in the exact simulation of a class of Piecewise Deterministic Markov Processes (PDMP). We show how to perform efficient thinning algorithms depending on the jump rate bound. For different types of jump rate bounds, we compare theoretically the mean number of generated (total) jump times and we compare numerically the simulation times. We use thinning algorithms on Hodgkin-Huxley models with Markovian ion channels dynamic to illustrate the results.

math.PR↗

arXiv2016

Limit theorems for weighted and regular Multilevel estimators

We aim at analyzing in terms of a.s. convergence and weak rate the performances of the Multilevel Monte Carlo estimator (MLMC) introduced in [Gil08] and of its weighted version, the Multilevel Richardson Romberg estimator (ML2R), introduced in [LP14]. These two estimators permit to compute a very accurate approximation of $I_0 = \mathbb{E}[Y_0]$ by a Monte Carlo type estimator when the (non-degenerate) random variable $Y_0 \in L^2(\mathbb{P})$ cannot be simulated (exactly) at a reasonable computational cost whereas a family of simulatable approximations $(Y_h)_{h \in \mathcal{H}}$ is available. We will carry out these investigations in an abstract framework before applying our results, mainly a Strong Law of Large Numbers and a Central Limit Theorem, to some typical fields of applications: discretization schemes of diffusions and nested Monte Carlo.

math.PR↗

arXiv2016

Multilevel Richardson-Romberg extrapolation

We propose and analyze a Multilevel Richardson-Romberg (MLRR) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg method introduced in [Pa07] and the variance control resulting from the stratification introduced in the Multilevel Monte Carlo (MLMC) method (see [Hei01, Gi08]). Thus, in standard frameworks like discretization schemes of diffusion processes, the root mean squared error (RMSE) $\varepsilon > 0$ can be achieved with our MLRR estimator with a global complexity of $\varepsilon^{-2} \log(1/\varepsilon)$ instead of $\varepsilon^{-2} (\log(1/\varepsilon))^2$ with the standard MLMC method, at least when the weak error $\mathbf{E}[Y_h]-\mathbf{E}[Y_0]$ of the biased implemented estimator $Y_h$ can be expanded at any order in $h$ and $\|Y_h - Y_0\|_2 = O(h^{\frac{1}{2}})$. The MLRR estimator is then halfway between a regular MLMC and a virtual unbiased Monte Carlo. When the strong error $\|Y_h - Y_0\|_2 = O(h^{\fracβ{2}})$, $β< 1$, the gain of MLRR over MLMC becomes even more striking. We carry out numerical simulations to compare these estimators in two settings: vanilla and path-dependent option pricing by Monte Carlo simulation and the less classical Nested Monte Carlo simulation.

math.PR↗