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A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects…
We study the $k$-largest eigenvalues of heavy-tailed sample covariance matrices of the form $\bX\bX^\T$ in an asymptotic framework, where the dimension of the data and the sample size tend to infinity. To this end, we assume that the rows…
In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
The Rasch model is the most prominent member of the class of latent trait models that are in common use. The main reason is that it can be considered as a measurement model that allows to separate person and item parameters, a feature that…
We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…
Large nonlinear recurrent neural networks with random couplings generate high-dimensional, potentially chaotic activity whose structure is of interest in neuroscience and other fields. A fundamental object encoding the collective structure…
Alpha-based performance evaluation may fail to capture correlated residuals due to model errors. This paper proposes using the Generalized Information Ratio (GIR) to measure performance under misspecified benchmarks. Motivated by the…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
Recent technological advancements have led to the rapid generation of high-throughput biological data, which can be used to address novel scientific questions in broad areas of research. These data can be thought of as a large matrix with…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
A new model for general cyclical long memory is introduced, by means of random modulation of certain bivariate long memory time series. This construction essentially decouples the two key features of cyclical long memory: quasi-periodicity…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
In causal inference, it is common to estimate the causal effect of a single treatment variable on an outcome. However, practitioners may also be interested in the effect of simultaneous interventions on multiple covariates of a fixed target…
The degree of static indeterminacy and its spatial distribution characterize load-bearing structures independent of a specific load case. The redundancy matrix stores the distribution of the static indeterminacy on its main diagonal, and…
We propose a batch size invariant version of Adam, for use in large-scale, distributed settings, in which the mini-batch is divided into micro-batches which are distributed among worker nodes. For the v term, standard Adam first computes…
This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and…
In observational studies, the causal effect of a treatment may be confounded with variables that are related to both the treatment and the outcome of interest. In order to identify a causal effect, such studies often rely on the…
The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss…