arXiv subjects

Armeen Taeb

Publications and source records attributed to Armeen Taeb.

21 records · Page 2Linked to original sources

arXiv2016

California Reservoir Drought Sensitivity and Exhaustion Risk Using Statistical Graphical Models

The ongoing California drought has highlighted the potential vulnerability of state water management infrastructure to multi-year dry intervals. Due to the high complexity of the network, dynamic storage changes across the California reservoir system have been difficult to model using either conventional statistical or physical approaches. Here, we analyze the interactions of monthly volumes in a network of 55 large California reservoirs, over a period of 136 months from 2004 to 2015, and we develop a latent-variable graphical model of their joint fluctuations. We achieve reliable and tractable modeling of the system because the model structure allows unique recovery of the best-in-class model via convex optimization with control of the number of free parameters. We extract a statewide `latent' influencing factor which turns out to be highly correlated with both the Palmer Drought Severity Index (PDSI, $ρ\approx 0.86$) and hydroelectric production ($ρ\approx 0.71$). Further, the model allows us to determine system health measures such as exhaustion probability and per-reservoir drought sensitivity. We find that as PDSI approaches -6, there is a probability greater than 50\% of simultaneous exhaustion of multiple large reservoirs.

stat.AP↗

arXiv2015

Sufficient Dimension Reduction and Modeling Responses Conditioned on Covariates: An Integrated Approach via Convex Optimization

Given observations of a collection of covariates and responses $(Y, X) \in \mathbb{R}^p \times \mathbb{R}^q$, sufficient dimension reduction (SDR) techniques aim to identify a mapping $f: \mathbb{R}^q \rightarrow \mathbb{R}^k$ with $k \ll q$ such that $Y|f(X)$ is independent of $X$. The image $f(X)$ summarizes the relevant information in a potentially large number of covariates $X$ that influence the responses $Y$. In many contemporary settings, the number of responses $p$ is also quite large, in addition to a large number $q$ of covariates. This leads to the challenge of fitting a succinctly parameterized statistical model to $Y|f(X)$, which is a problem that is usually not addressed in a traditional SDR framework. In this paper, we present a computationally tractable convex relaxation based estimator for simultaneously (a) identifying a linear dimension reduction $f(X)$ of the covariates that is sufficient with respect to the responses, and (b) fitting several types of structured low-dimensional models -- factor models, graphical models, latent-variable graphical models -- to the conditional distribution of $Y|f(X)$. We analyze the consistency properties of our estimator in a high-dimensional scaling regime. We also illustrate the performance of our approach on a newsgroup dataset and on a dataset consisting of financial asset prices.

stat.ME↗

arXiv2013

Maximin Analysis of Message Passing Algorithms for Recovering Block Sparse Signals

We consider the problem of recovering a block (or group) sparse signal from an underdetermined set of random linear measurements, which appear in compressed sensing applications such as radar and imaging. Recent results of Donoho, Johnstone, and Montanari have shown that approximate message passing (AMP) in combination with Stein's shrinkage outperforms group LASSO for large block sizes. In this paper, we prove that, for a fixed block size and in the strong undersampling regime (i.e., having very few measurements compared to the ambient dimension), AMP cannot improve upon group LASSO, thereby complementing the results of Donoho et al.

cs.IT↗