Related papers: Sparse estimation for generalized exponential mark…

The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…

We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…

Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations…

An extension of the Hawkes model where the productivity is variable is considered. In particular, the case is considered where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood…

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…

The Hawkes model is a past-dependent point process, widely used in various fields for modeling temporal clustering of events. Extending this framework, the multidimensional marked Hawkes process incorporates multiple interacting event types…

This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…

This work is concern with testing the low-dimensional parameters of interest with divergent dimensional data and variable selection for the rest under the sparse case. A consistent test via the partial penalized likelihood approach, called…

An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive…

Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…

This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…

The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

Linear multivariate Hawkes processes (MHP) are a fundamental class of point processes with self-excitation. When estimating parameters for these processes, a difficulty is that the two main error functionals, the log-likelihood and the…

We consider the nonparametric regression and the classification problems for $\psi$-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, $\ldots$. A penalized estimation…

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose…

In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…