arXiv subjects

Anirudh Rayas

Publications and source records attributed to Anirudh Rayas.

5 recordsLinked to original sources

arXiv2026

MiGHT-EHR: A Multi-task Graph Transformer for Heterogeneous Temporal Electronic Health Records

Learning from Electronic Health Records (EHRs) has gained significant attention due to its potential to improve clinical prediction. However, effective learning remains challenging because EHRs encode heterogeneous, temporally ordered clinical interactions. In particular, EHRs contain: (i) heterogeneous clinical entities, including patients, visits, diagnoses, prescriptions, and procedures, together with their heterogeneous interactions, (ii) longitudinal patient trajectories across hospital visits and (iii) shared statistical dependencies across related clinical prediction tasks. Existing EHR learning methods capture only a subset of these properties. To bridge this gap, we propose Multi-task Graph transformer for Heterogeneous Temporal EHRs (MiGHT-EHR), which jointly models all three within a unified representation learning method. MiGHT-EHR constructs a heterogeneous graph from EHRs in which nodes represent clinical entities and edges connect statistically associated entities identified via normalized point-wise mutual information. Across MIMIC-III and MIMIC-IV datasets, MiGHT-EHR outperforms state-of-the-art methods on average across four tasks: drug recommendation, prediction of length-of-stay, mortality, and readmission, with particularly strong improvements in mortality and readmission prediction. Furthermore, a post-hoc analysis of the learned representations reveals that patient neighborhoods are organized by clinical outcomes, salient medical concepts are recoverable as linear directions in the representation space, and task probabilities are well calibrated. Collectively, these findings demonstrate that MiGHT-EHR representations support diverse prediction tasks while preserving clinically interpretable structure.

cs.LG↗

arXiv2024

Local and Mixing-Based Algorithms for Gaussian Graphical Model Selection from Glauber Dynamics

Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian Glauber dynamics. We develop two complementary approaches. The first is a local edge-testing estimator based on an appropriately designed correlation test that reveals edges. This estimator does not require waiting for the chain to mix and admits an embarrassingly parallel edgewise implementation. The second is a burn-in/thinning reduction: under a Dobrushin contraction condition, we prove that a suitably subsampled Gaussian Gibbs trajectory is close in total variation to an i.i.d. product sample, allowing standard i.i.d. Gaussian graphical model learners to be used as black boxes. The key technical ingredient, which may be of independent interest, is a high-dimensional total-variation bound for random-scan Gaussian Gibbs samplers, obtained by combining Wasserstein contraction with an approximate Lipschitz smoothing argument. We prove finite-sample recovery guarantees for both approaches, establish information-theoretic lower bounds on the observation time, and empirically compare the resulting sample-computation tradeoffs.

cs.LG↗

arXiv2024

Learning Networks from Wide-Sense Stationary Stochastic Processes

Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by steady-state linear conservation laws: $X_t = {L^{\ast}}Y_{t}$, where $X_t, Y_t \in \mathbb{R}^p$ denote inputs and potentials, respectively, and the sparsity pattern of the $p \times p$ Laplacian $L^{\ast}$ encodes the edge structure. Assuming $X_t$ to be a wide-sense stationary stochastic process with a known spectral density matrix, we learn the support of $L^{\ast}$ from temporally correlated samples of $Y_t$ via an $\ell_1$-regularized Whittle's maximum likelihood estimator (MLE). The regularization is particularly useful for learning large-scale networks in the high-dimensional setting where the network size $p$ significantly exceeds the number of samples $n$. We show that the MLE problem is strictly convex, admitting a unique solution. Under a novel mutual incoherence condition and certain sufficient conditions on $(n, p, d)$, we show that the ML estimate recovers the sparsity pattern of $L^\ast$ with high probability, where $d$ is the maximum degree of the graph underlying $L^{\ast}$. We provide recovery guarantees for $L^\ast$ in element-wise maximum, Frobenius, and operator norms. Finally, we complement our theoretical results with several simulation studies on synthetic and benchmark datasets, including engineered systems (power and water networks), and real-world datasets from neural systems (such as the human brain).

stat.ML↗

arXiv2023

Differential Analysis for Networks Obeying Conservation Laws

Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion consensus. Such conservation laws are often modeled as balance equations that relate appropriate injected flows and potentials at the nodes of the networks. A recent line of work considers the problem of estimating the unknown structure of such networked systems from observations of node potentials (and only the knowledge of the statistics of injected flows). Given the dynamic nature of the systems under consideration, an equally important task is estimating the change in the structure of the network from data -- the so called differential network analysis problem. That is, given two sets of node potential observations, the goal is to estimate the structural differences between the underlying networks. We formulate this novel differential network analysis problem for systems obeying conservation laws and devise a convex estimator to learn the edge changes directly from node potentials. We derive conditions under which the estimate is unique in the high-dimensional regime and devise an efficient ADMM-based approach to perform the estimation. Finally, we demonstrate the performance of our approach on synthetic and benchmark power network data.

eess.SY↗

arXiv2022

Learning the Structure of Large Networked Systems Obeying Conservation Laws

Many networked systems such as electric networks, the brain, and social networks of opinion dynamics are known to obey conservation laws. Examples of this phenomenon include the Kirchoff laws in electric networks and opinion consensus in social networks. Conservation laws in networked systems may be modeled as balance equations of the form $X = B^{*} Y$, where the sparsity pattern of $B^{*}$ captures the connectivity of the network, and $Y, X \in \mathbb{R}^p$ are vectors of "potentials" and "injected flows" at the nodes respectively. The node potentials $Y$ cause flows across edges and the flows $X$ injected at the nodes are extraneous to the network dynamics. In several practical systems, the network structure is often unknown and needs to be estimated from data. Towards this, one has access to samples of the node potentials $Y$, but only the statistics of the node injections $X$. Motivated by this important problem, we study the estimation of the sparsity structure of the matrix $B^{*}$ from $n$ samples of $Y$ under the assumption that the node injections $X$ follow a Gaussian distribution with a known covariance $\Sigma_X$. We propose a new $\ell_{1}$-regularized maximum likelihood estimator for this problem in the high-dimensional regime where the size of the network $p$ is larger than sample size $n$. We show that this optimization problem is convex in the objective and admits a unique solution. Under a new mutual incoherence condition, we establish sufficient conditions on the triple $(n,p,d)$ for which exact sparsity recovery of $B^{*}$ is possible with high probability; $d$ is the degree of the graph. We also establish guarantees for the recovery of $B^{*}$ in the element-wise maximum, Frobenius, and operator norms. Finally, we complement these theoretical results with experimental validation of the performance of the proposed estimator on synthetic and real-world data.

stat.ML↗