Related papers: On global identification in structural vector auto…
The paper provides a parametrization of Vector Autoregression (VAR) that enables one to look at the parameters associated with unit root dynamics and those associated with stable dynamics separately. The task is achieved via a novel…
The performance of sparse matrix computation highly depends on the matching of the matrix format with the underlying structure of the data being computed on. Different sparse matrix formats are suitable for different structures of data.…
Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some…
We establish necessary and sufficient conditions for the existence of an LU factorization $A=LU$ for an arbitrary square matrix $A$, including singular and rank-deficient cases, without the use of row or column permutations. We prove that…
This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries…
Random matrices are widely used in sparse recovery problems, and the relevant properties of matrices with i.i.d. entries are well understood. The current paper discusses the recently introduced Restricted Eigenvalue (RE) condition, which is…
The problem of combinatorially determining the rank of the 3-dimensional bar-joint {\em rigidity matroid} of a graph is an important open problem in combinatorial rigidity theory. Maxwell's condition states that the edges of a graph $G=(V,…
High-dimensional settings, where the data dimension ($d$) far exceeds the number of observations ($n$), are common in many statistical and machine learning applications. Methods based on $\ell_1$-relaxation, such as Lasso, are very popular…
Structural causal models provide a unified semantics for interventions and counterfactuals, but most identifiability results rely on restrictive assumptions like global monotonicity, which are often violated in embodied interaction, where…
This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure…
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global…
This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the low-rank matrix completion problem with…
We develop a pseudo-likelihood theory for rank one matrix estimation problems in the high dimensional limit. We prove a variational principle for the limiting pseudo-maximum likelihood which also characterizes the performance of the…
We study the rank-three lifting problem for incidence matrices of finite projective planes through residue-level determinant constraints invisible to tropical valuations alone. In residue characteristic $\neq 3$, any rank-$\le 3$ lift of…
We consider the most common variants of linear regression, including Ridge, Lasso and Support-vector regression, in a setting where the learner is allowed to observe only a fixed number of attributes of each example at training time. We…
The standard vector autoregressive (VAR) models suffer from overparameterization which is a serious issue for high-dimensional time series data as it restricts the number of variables and lags that can be incorporated into the model.…
We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
We study identification in structural vector autoregressions (SVARs) in which the endogenous variables enter nonlinearly on the left-hand side of the model, a feature we term endogenous nonlinearity, to distinguish it from the more familiar…
It is natural to ask: what kinds of matrices satisfy the Restricted Eigenvalue (RE) condition? In this paper, we associate the RE condition (Bickel-Ritov-Tsybakov 09) with the complexity of a subset of the sphere in $\R^p$, where $p$ is the…