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Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…
This paper presents a comprehensive exploration of the theoretical properties inherent in the Adaptive Lasso and the Transfer Lasso. The Adaptive Lasso, a well-established method, employs regularization divided by initial estimators and is…
The quasi-maximum likelihood estimation is a commonly-used method for estimating GARCH parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…
Sparse feature selection has been demonstrated to be effective in handling high-dimensional data. While promising, most of the existing works use convex methods, which may be suboptimal in terms of the accuracy of feature selection and…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows the parametric estimation, including the change-points, and automatic variable…
This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving…
We consider model selection in generalized linear models (GLM) for high-dimensional data and propose a wide class of model selection criteria based on penalized maximum likelihood with a complexity penalty on the model size. We derive a…
The Poisson log-normal model is a latent variable model that provides a generic framework for the analysis of multivariate count data. Inferring its parameters can be a daunting task since the conditional distribution of the latent…
We introduce a general semiparametric clusterwise elliptical distribution to assess how latent cluster structure shapes continuous outcomes. Using a subjectwise representation, we first estimate cluster-specific mean vectors and a…
Downsampling or under-sampling is a technique that is utilized in the context of large and highly imbalanced classification models. We study optimal downsampling for imbalanced classification using generalized linear models (GLMs). We…
We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we…
The aim of this paper is to estimate the density f of a random variable X when one has access to independent observations of the sum of K $\ge$ 2 independent copies of X. We provide a constructive estimator based on a suitable definition of…
To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous…
Generalized Linear Mixed Models (GLMMs) are widely used for analysing clustered data. One well-established method of overcoming the integral in the marginal likelihood function for GLMMs is penalized quasi-likelihood (PQL) estimation,…
In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…
The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
Individuals or companies in a large social or financial network often display rather heterogeneous behaviors for various reasons. In this work, we propose a network vector autoregressive model with a latent group structure to model…