Related papers: Low Rank and Structured Modeling of High-dimension…

We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise…

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…

Modern large language models are increasingly deployed under compute and memory constraints, making flexible control of model capacity a central challenge. While sparse and low-rank structures naturally trade off capacity and performance,…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…

Jointly modeling and forecasting economic and financial variables across a large set of countries has long been a significant challenge. Two primary approaches have been utilized to address this issue: the vector autoregressive model with…

The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of AR coefficients can be prohibitively large, resulting in…

We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles…

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…

Under a high-dimensional vector autoregressive (VAR) model, we propose a way of efficiently estimating both the stationary graph structure between the nodal time series and their temporal dynamics. The framework is then used to make…

The R package BigVAR allows for the simultaneous estimation of high-dimensional time series by applying structured penalties to the conventional vector autoregression (VAR) and vector autoregression with exogenous variables (VARX)…

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed…

Multi-relational networks among entities are frequently observed in the era of big data. Quantifying the effects of multiple networks have attracted significant research interest recently. In this work, we model multiple network effects…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

The sparse group lasso is a high-dimensional regression technique that is useful for problems whose predictors have a naturally grouped structure and where sparsity is encouraged at both the group and individual predictor level. In this…

Modeling responses on the nodes of a large-scale network is an important task that arises commonly in practice. This paper proposes a community network vector autoregressive (CNAR) model, which utilizes the network structure to characterize…

Networks are a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the…

Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to…

Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural…