Related papers: The Functional Graphical Lasso
We construct a N-dimensional Gaussian landscape with multiscale, translation invariant, logarithmic correlations and investigate the statistical mechanics of a single particle in this environment. In the limit of high dimension N>>1 the…
We propose a method for recovering the structure of a sparse undirected graphical model when very few samples are available. The method decides about the presence or absence of bonds between pairs of variable by considering one pair at a…
Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…
In this paper we develop valid inference for high-dimensional time series. We extend the desparsified lasso to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
A central question in modern machine learning and imaging sciences is to quantify the number of effective parameters of vastly over-parameterized models. The degrees of freedom is a mathematically convenient way to define this number of…
We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…
The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal…
We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support…
In many applications of finance, biology and sociology, complex systems involve entities interacting with each other. These processes have the peculiarity of evolving over time and of comprising latent factors, which influence the system…
Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…
Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…
We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in…
We consider tests of significance in the setting of the graphical lasso for inverse covariance matrix estimation. We propose a simple test statistic based on a subsequence of the knots in the graphical lasso path. We show that this…
We study the limitations of the well known LASSO regression as a variable selector when there exists dependence structures among covariates. We analyze both the classic situation with $n\geq p$ and the high dimensional framework with $p>n$.…
We propose a generalization of the lasso that allows the model coefficients to vary as a function of a general set of modifying variables. These modifiers might be variables such as gender, age or time. The paradigm is quite general, with…
Fitting a graphical model to a collection of random variables given sample observations is a challenging task if the observed variables are influenced by latent variables, which can induce significant confounding statistical dependencies…