Related papers: Segmentation of multiple series using a Lasso stra…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
Smooth dynamics interrupted by discontinuities are known as hybrid systems and arise commonly in nature. Latent ODEs allow for powerful representation of irregularly sampled time series but are not designed to capture trajectories arising…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
Corrupted sensing concerns the problem of recovering a high-dimensional structured signal from a collection of measurements that are contaminated by unknown structured corruption and unstructured noise. In the case of linear measurements,…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
We consider the segmentation of set of correlated time-series, the correlation being allowed to take an arbitrary form but being the same at each time-position. We show that encoding the dependency in a factor model enables us to use the…
Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…
Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. In this article, the problem of detecting…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…
We propose a new technique for consistent estimation of the number and locations of the change-points in the structure of an irregularly spaced time series. The core of the segmentation procedure is the Ensemble Binary Segmentation method…
A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time…
Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…
We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multi-way data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner…
We propose a new nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second- order) piecewise stationary process, which also identifies the components of…
Sensor devices have been increasingly used in engineering and health studies recently, and the captured multi-dimensional activity and vital sign signals can be studied in association with health outcomes to inform public health. The common…
Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…
We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…
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…