Segmentation of the mean of heteroscedastic data via cross-validation

Arlot, Sylvain; Célisse, Alain

doi:10.1007/s11222-010-9196-x

Cited by 40 publications

(40 citation statements)

References 51 publications

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“…For the LASSO estimator defined in (2), two types of prediction bounds are known in the literature. The first type is termed a "fast-rate bound."…”

Section: Review Of Bounds For Lasso-type Estimatorsmentioning

confidence: 99%

“…data and the risk is in out-of-sample prediction (as compared to the in-sample prediction considered here) for a sample size smaller than n (since cross-validation involves data splitting). A comprehensive overview of cross-validation theory can be found in [1], further ideas in [2] and others. Nevertheless, there are currently no non-asymptotic guarantees for LASSO-type estimators calibrated by k-fold cross-validation.…”

Section: Assumptionmentioning

confidence: 99%

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Prediction error bounds for linear regression with the TREX

Bien

Gaynanova

Lederer

et al. 2018

TEST

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The TREX is a recently introduced approach to sparse linear regression. In contrast to most well-known approaches to penalized regression, the TREX can be formulated without the use of tuning parameters. In this paper, we establish the first known prediction error bounds for the TREX. Additionally, we introduce extensions of the TREX to a more general class of penalties, and we provide a bound on the prediction error in this generalized setting. These results deepen the understanding of TREX from a theoretical perspective and provide new insights into penalized regression in general.

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“…For the LASSO estimator defined in (2), two types of prediction bounds are known in the literature. The first type is termed a "fast-rate bound."…”

Section: Review Of Bounds For Lasso-type Estimatorsmentioning

confidence: 99%

Section: Assumptionmentioning

confidence: 99%

Prediction error bounds for linear regression with the TREX

Bien

Gaynanova

Lederer

et al. 2018

TEST

View full text Add to dashboard Cite

show abstract

“…Detecting changes in the mean with the Gaussian kernel Let us consider the archetypic change-point detection problem -finding changes in the mean of a sequence of independent random variables-and show how these changes are localized more precisely when more data are available. We define three functions µ m : [0, 1] → R, 1 ≤ m ≤ 3, previously used by Arlot and Celisse [3], which cover a variety of situations (see Fig. 4).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Consistent change-point detection with kernels

Garreau¹,

Arlot²

2018

Electron. J. Statist.

Self Cite

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In this paper we study the kernel change-point algorithm (KCP) proposed by Arlot, Celisse and Harchaoui [4], which aims at locating an unknown number of change-points in the distribution of a sequence of independent data taking values in an arbitrary set. The change-points are selected by model selection with a penalized kernel empirical criterion. We provide a non-asymptotic result showing that, with high probability, the KCP procedure retrieves the correct number of change-points, provided that the constant in the penalty is well-chosen; in addition, KCP estimates the change-points location at the optimal rate. As a consequence, when using a characteristic kernel, KCP detects all kinds of change in the distribution (not only changes in the mean or the variance), and it is able to do so for complex structured data (not necessarily in R d ). Most of the analysis is conducted assuming that the kernel is bounded; part of the results can be extended when we only assume a finite second-order moment.MSC 2010 subject classifications: Primary 62M10; secondary 62G20.

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“…Many segmentation time series methods were developed [16,17,18], most of these methods are based on dynamic programming in order to reduce the number of obtained segments. However, in our situation, we are interested only by the detection of the first and the second segments (just to know if the time series increases or decreases).…”

Section: Time Series Segmentation and Detection Of Transition Pointsmentioning

confidence: 99%

Hidden Markov Models for Modeling Occurrence Order of Facial Temporal Dynamics

Ghanem

2013

Advanced Concepts for Intelligent Vision Systems

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Abstract. The analysis of facial expression temporal dynamics is of great importance for many real-world applications. Furthermore, due to the variability among individuals and different contexts, the dynamic relationships among facial features are stochastic. Systematically capturing such temporal dependencies among facial features and incorporating them into the facial expression recognition process is especially important for interpretation and understanding of facial behaviors. The base system in this paper uses Hidden Markov Models (HMMs) and a new set of derived features from geometrical distances obtained from detected and automatically tracked facial points. We propose here to transform numerical representation which is in the form of multi time series to a symbolic representation in order to reduce dimensionality, extract the most pertinent information and give a meaningful representation to human. Experiments show that new and interesting results have been obtained from the proposed approach.Keywords: Facial expression, HMM, Occurrence order, time series. IntroductionAnalyzing the dynamic of facial features and (or) the changes in the appearance of facial features (eye, eyebrows and mouth) is a very important step in facial expression understanding and interpretation. Many researchers attempt to study the dynamic behavior. Timing, duration, speed and occurrence order in which the temporal segment of the different face/body actions occur are crucial parameters related to dynamic behavior [1]. Timing, duration and speed have been analyzed in several studies [2,3,4,5]. Little attention has been given to occurrence order [3,5]. In this paper we propose to explicitly analyze one aspect of facial dynamics by detecting the occurrence order in which facial features movement occurs. For example, expressions typically associated with happiness contain AU6 and AU12, the fact is that is not known in which order each AU occur, this is what we want to discover.As it is known, a facial expression recognition system consists generally of three steps: pre-processing, feature extraction and classification. In this paper we are not interested by the first step which relates to face localization, and registration to remove the variability due to changes in head pose and illumination.

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Segmentation of the mean of heteroscedastic data via cross-validation

Cited by 40 publications

References 51 publications

Prediction error bounds for linear regression with the TREX

Prediction error bounds for linear regression with the TREX

Consistent change-point detection with kernels

Hidden Markov Models for Modeling Occurrence Order of Facial Temporal Dynamics

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