arXiv subjects

George Michailidis

Publications and source records attributed to George Michailidis.

At least 19 recordsLinked to original sources

arXiv2026

OTAP: Structure-Aware Optimal Transport for Evaluating Planning and Execution in Agent Trajectories

Large language model agents solve tasks by generating trajectories that interleave planning, tool calls, and intermediate results. Current evaluation metrics reduce such a trajectory to a binary success flag, compare it against a reference by exact matching, or delegate judgment to another language model. A success flag cannot distinguish a sound solution from one that succeeds by luck, and says nothing about why a failed run went wrong. Exact matching penalizes plans that are valid but reordered or decomposed differently from the reference. We reframe trajectory evaluation as a distance between the agent's execution graph and a set of valid solution graphs, and instantiate it via an unbalanced fused Gromov-Wasserstein transport problem over attributed dependency graphs. The resulting score, termed OTAP (Optimal Transport for Agentic Planning), is a pseudo-metric that is provably invariant to dependency-preserving reorderings and has bounded sensitivity to redundant steps. Its unbalanced marginals handle missing or hallucinated steps without forcing a match, and its soft coupling accommodates variation in plan granularity. On controlled perturbations and three public benchmarks, OTAP separates valid from invalid trajectories in a regime where semantics-only metrics score below chance. Its advantage tracks the fidelity of the dependency graph: largest where edges follow from operator semantics, smallest where they are inferred from free text. Where a formal verifier exists, strict surface metrics predict validity better than OTAP does, which places OTAP in open-ended domains where no verifier is available.

cs.AI↗

arXiv2026

Localized LoRA-MoE: Block-wise Low-Rank Experts With Adaptive Routing

Large Language Models (LLMs) and high-dimensional perception networks increasingly rely on parameter-efficient fine-tuning (PEFT) to adapt to diverse operational contexts. However, standard methods like LoRA are structurally limited by a monolithic bottleneck, making them highly susceptible to gradient warfare. Interleaved multi-task streams may trigger destructive optimization feedback, collapsing adapter weights into unspecialized averages. While recent spatial partitioning methods have introduced block-wise isolation, they remain trapped in static topologies, unable to adapt to dynamic task-switching or environmental sensor failure. In this work, we introduce Localized LoRA-MoE, a unified framework that fuses localized spatial blocking with dynamic, context-conditioned routing. We propose and evaluate two novel architectural paradigms: Block-Wise LoRA-MoE (Centralized Macro-Routing), which modulates the entire structural grid via a monolithic context signal, and Cell-Wise LoRA-MoE (Decentralized Micro-Routing), which empowers every coordinate cell in the matrix grid with autonomous, localized expert gating. Through a comprehensive suite of benchmarks, ranging from high-dimensional SVD matrix simulations and real-world tabular transformations to spatial vision perception under sensor degradation, we demonstrate that both architectures resolve optimization deadlocks inherent in static baselines. Our empirical results establish that decentralized cell-level gating achieves complete statistical parity with an omniscient global coordinator, providing a robust "gradient firewall" that protects surviving pathways from fault-propagated corruption. Our proposals consistently outperform static baselines, offering a scalable and parameter-efficient solution for dynamic model adaptation across granular coordinate fields and shifting operational regimes.

cs.LG↗

arXiv2026

Equilibrium and Pricing in Consumer Networks with Nonlinear Utilities: An Online Shape-Constrained Learning Approach

We study optimal monopoly pricing over consumer networks governed by general nonlinear utilities. In our framework, a consumer's utility is jointly determined by an individualized price and the consumption choices of their peers, propagated through a directed and signed social graph. This formulation encapsulates a broad class of utility functions; it strictly generalizes the traditional linear-quadratic framework to include logit-type discrete choice, isoelastic, and Stone-Geary utilities under a single theoretical umbrella. We first establish the existence and uniqueness of the consumer-side equilibrium under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities. Leveraging this equilibrium characterization, we analyze targeted price discrimination within community-structured and influencer-driven markets. To this end, we introduce a generalized measure of network influence that extends classical Katz-Bonacich centrality beyond the Euclidean domain. Finally, addressing the challenge of unknown consumer utility functions, we develop a shape-constrained, tuning-parameter-free learning approach utilizing isotonic regression, for which we establish strict no-regret convergence guarantees. Supported by extensive simulations, our results seamlessly integrate equilibrium analysis and nonparametric learning into a cohesive monopoly pricing framework.

math.ST↗

arXiv2026

Fast localization of anomalous patches in spatial data under dependence

We propose a scalable, provably accurate method for localizing an unknown number of multiple axis-aligned anomalous patches in spatial data under a general class of spatial dependence. Motivated by the practical need to detect localized changes rather than completely segment large spatial grids, we first introduce both a naive and a significantly faster intelligent-sampling-based estimator for a single patch. We then extend this methodology to the highly challenging multiple-patch setting and propose a two-stage Spatial Patch Localization of Anomalies under DEpendence procedure (SPLADE). Under mild conditions on signal strength, separation from the boundary, inter-patch separation, and a uniform Gaussian approximation, we establish simultaneous consistency for the estimated number of patches and for each individual patch boundary. Extensive numerical results based on synthetic data scenarios demonstrate that the proposed method exhibits significant computational and accuracy gains over competing approaches, as well as robustness to moderate and severe spatial dependence. Finally, we demonstrate the real-world utility of the proposed method by applying it to frame-to-frame video surveillance data, where it accurately detects small, closely separated subjects, a task where existing methods are significantly slower and highly prone to spurious detections due to not accounting for spatial dependence. A second application on 3D fibrous media is deferred to the Appendix.

stat.ME↗

arXiv2025

Stochastic Regret Guarantees for Online Zeroth- and First-Order Bilevel Optimization

Online bilevel optimization (OBO) is a powerful framework for machine learning problems where both outer and inner objectives evolve over time, requiring dynamic updates. Current OBO approaches rely on deterministic \textit{window-smoothed} regret minimization, which may not accurately reflect system performance when functions change rapidly. In this work, we introduce a novel search direction and show that both first- and zeroth-order (ZO) stochastic OBO algorithms leveraging this direction achieve sublinear {stochastic bilevel regret without window smoothing}. Beyond these guarantees, our framework enhances efficiency by: (i) reducing oracle dependence in hypergradient estimation, (ii) updating inner and outer variables alongside the linear system solution, and (iii) employing ZO-based estimation of Hessians, Jacobians, and gradients. Experiments on online parametric loss tuning and black-box adversarial attacks validate our approach.

cs.LG↗

arXiv2025

Joint Learning of Panel VAR models with Low Rank and Sparse Structure

Panel vector auto-regressive (VAR) models are widely used to capture the dynamics of multivariate time series across different subpopulations, where each subpopulation shares a common set of variables. In this work, we propose a panel VAR model with a shared low-rank structure, modulated by subpopulation-specific weights, and complemented by idiosyncratic sparse components. To ensure parameter identifiability, we impose structural constraints that lead to a nonsmooth, nonconvex optimization problem. We develop a multi-block Alternating Direction Method of Multipliers (ADMM) algorithm for parameter estimation and establish its convergence under mild regularity conditions. Furthermore, we derive consistency guarantees for the proposed estimators under high-dimensional scaling. The effectiveness of the proposed modeling framework and estimators is demonstrated through experiments on both synthetic data and a real-world neuroscience data set.

stat.ME↗

arXiv2025

Normalizing Flow to Augmented Posterior: Conditional Density Estimation with Interpretable Dimension Reduction for High Dimensional Data

The conditional density characterizes the distribution of a response variable $y$ given other predictor $x$, and plays a key role in many statistical tasks, including classification and outlier detection. Although there has been abundant work on the problem of Conditional Density Estimation (CDE) for a low-dimensional response in the presence of a high-dimensional predictor, little work has been done for a high-dimensional response such as images. The promising performance of normalizing flow (NF) neural networks in unconditional density estimation acts a motivating starting point. In this work, we extend NF neural networks when external $x$ is present. Specifically, they use the NF to parameterize a one-to-one transform between a high-dimensional $y$ and a latent $z$ that comprises two components $[z_P,z_N]$. The $z_P$ component is a low-dimensional subvector obtained from the posterior distribution of an elementary predictive model for $x$, such as logistic/linear regression. The $z_N$ component is a high-dimensional independent Gaussian vector, which explains the variations in $y$ not or less related to $x$. Unlike existing CDE methods, the proposed approach, coined Augmented Posterior CDE (AP-CDE), only requires a simple modification on the common normalizing flow framework, while significantly improving the interpretation of the latent component, since $z_P$ represents a supervised dimension reduction. In image analytics applications, AP-CDE shows good separation of $x$-related variations due to factors such as lighting condition and subject id, from the other random variations. Further, the experiments show that an unconditional NF neural network, based on an unsupervised model of $z$, such as Gaussian mixture, fails to generate interpretable results.

stat.ME↗

arXiv2025

Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning

Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, offer compact and effective alternatives to full model fine-tuning by introducing low-rank updates to pre-trained weights. However, most existing approaches rely on global low rank structures, which can overlook spatial patterns spread across the parameter space. In this work, we propose Localized LoRA, a generalized framework that models weight updates as a composition of low-rank matrices applied to structured blocks of the weight matrix. This formulation enables dense, localized updates throughout the parameter space without increasing the total number of trainable parameters. We provide a formal comparison between global, diagonal-local, and fully localized low-rank approximations, and show that our method consistently achieves lower approximation error under matched parameter budgets. Experiments on both synthetic and practical settings demonstrate that Localized LoRA offers a more expressive and adaptable alternative to existing methods, enabling efficient fine-tuning with improved performance.

cs.LG↗

arXiv2025

Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and investigate a deep neural network-based approach to estimate it. The method allows for flexible functional dependency on the covariate, and fits the data reasonably well in the absence of a Gaussianity assumption. Theoretical results with PAC guarantees are established for the method, under assumptions commonly used in an Empirical Risk Minimization framework. The performance of the proposed method is evaluated on several synthetic data settings and benchmarked against existing approaches. The method is further illustrated on real datasets involving data from neuroscience and finance, respectively, and produces interpretable results.

stat.ML↗

arXiv2025

Neural Network-Based Change Point Detection for Large-Scale Time-Evolving Data

The paper studies the problem of detecting and locating change points in multivariate time-evolving data. The problem has a long history in statistics and signal processing and various algorithms have been developed primarily for simple parametric models. In this work, we focus on modeling the data through feed-forward neural networks and develop a detection strategy based on the following two-step procedure. In the first step, the neural network is trained over a prespecified window of the data, and its test error function is calibrated over another prespecified window. Then, the test error function is used over a moving window to identify the change point. Once a change point is detected, the procedure involving these two steps is repeated until all change points are identified. The proposed strategy yields consistent estimates for both the number and the locations of the change points under temporal dependence of the data-generating process. The effectiveness of the proposed strategy is illustrated on synthetic data sets that provide insights on how to select in practice tuning parameters of the algorithm and in real data sets. Finally, we note that although the detection strategy is general and can work with different neural network architectures, the theoretical guarantees provided are specific to feed-forward neural architectures.

stat.ML↗

arXiv2024

Deep Learning-based Approaches for State Space Models: A Selective Review

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

stat.ML↗

arXiv2024

A generalized Bayesian approach for high-dimensional robust regression with serially correlated errors and predictors

This paper introduces a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which smooths the well-known Huber loss, effectively balancing quadratic ($\ell_2$) and absolute linear ($\ell_1$) loss behaviors. This flexibility enables the framework to accommodate both thin-tailed and heavy-tailed data efficiently. The generalized Bayesian approach constructs a working likelihood based on the SPH loss, facilitating efficient and stable estimation while providing rigorous uncertainty quantification for all model parameters. Notably, this approach allows formal statistical inference without requiring ad hoc tuning parameter selection while adaptively addressing a wide range of tail behavior in the errors. By specifying appropriate prior distributions for the regression coefficients--such as ridge priors for small or moderate-dimensional settings and spike-and-slab priors for high-dimensional settings--the framework ensures principled inference. We establish rigorous theoretical guarantees for accurate parameter estimation and correct predictor selection under sparsity assumptions for a wide range of data generating setups. Extensive simulation studies demonstrate the superior performance of our approach compared to traditional Bayesian regression methods based on $\ell_2$ and $\ell_1$-loss functions. The results highlight its flexibility and robustness, particularly in challenging high-dimensional settings characterized by data contamination.

stat.ME↗

arXiv2024

A VAE-based Framework for Learning Multi-Level Neural Granger-Causal Connectivity

Granger causality has been widely used in various application domains to capture lead-lag relationships amongst the components of complex dynamical systems, and the focus in extant literature has been on a single dynamical system. In certain applications in macroeconomics and neuroscience, one has access to data from a collection of related such systems, wherein the modeling task of interest is to extract the shared common structure that is embedded across them, as well as to identify the idiosyncrasies within individual ones. This paper introduces a Variational Autoencoder (VAE) based framework that jointly learns Granger-causal relationships amongst components in a collection of related-yet-heterogeneous dynamical systems, and handles the aforementioned task in a principled way. The performance of the proposed framework is evaluated on several synthetic data settings and benchmarked against existing approaches designed for individual system learning. The method is further illustrated on a real dataset involving time series data from a neurophysiological experiment and produces interpretable results.

cs.LG↗

arXiv2024

A Functional Coefficients Network Autoregressive Model

The paper introduces a flexible model for the analysis of multivariate nonlinear time series data. The proposed Functional Coefficients Network Autoregressive (FCNAR) model considers the response of each node in the network to depend in a nonlinear fashion to each own past values (autoregressive component), as well as past values of each neighbor (network component). Key issues of model stability/stationarity, together with model parameter identifiability, estimation and inference are addressed for error processes that can be heavier than Gaussian for both fixed and growing number of network nodes. The performance of the estimators for the FCNAR model is assessed on synthetic data and the applicability of the model is illustrated on multiple indicators of air pollution data.

stat.ME↗

arXiv2023

Structural Discovery with Partial Ordering Information for Time-Dependent Data with Convergence Guarantees

Structural discovery amongst a set of variables is of interest in both static and dynamic settings. In the presence of lead-lag dependencies in the data, the dynamics of the system can be represented through a structural equation model (SEM) that simultaneously captures the contemporaneous and temporal relationships amongst the variables, with the former encoded through a directed acyclic graph (DAG) for model identification. In many real applications, a partial ordering amongst the nodes of the DAG is available, which makes it either beneficial or imperative to incorporate it as a constraint in the problem formulation. This paper develops an algorithm that can seamlessly incorporate a priori partial ordering information for solving a linear SEM (also known as Structural Vector Autoregression) under a high-dimensional setting. The proposed algorithm is provably convergent to a stationary point, and exhibits competitive performance on both synthetic and real data sets.

stat.ME↗

arXiv2023

Cardinality Constrained Mean-Variance Portfolios: A Penalty Decomposition Algorithm

The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of solving this problem directly, many existing methods rely on regularization and approximation techniques, which hinder investors' ability to precisely specify a portfolio's desired cardinality level. Moreover, these approaches typically include more hyper-parameters and increase the problem's dimensionality. To address these challenges, we propose a customized penalty decomposition algorithm. We demonstrate that this algorithm not only does it converge to a local minimizer of the cardinality-constrained mean-variance portfolio problem, but is also computationally efficient. Our approach leverages a sequence of penalty subproblems, each tackled using Block Coordinate Descent (BCD). Specifically, we show that the steps within BCD yield closed-form solutions, allowing us to identify a saddle point of the penalty subproblems. Finally, by applying our penalty decomposition algorithm to real-world datasets, we highlight its efficiency and its superiority over state-of-the-art methods across several performance metrics.

math.OC↗

arXiv2023

Low Tree-Rank Bayesian Vector Autoregression Model

Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good forecasting performance. However, in many data applications, such as those in neuroscience, the Granger causality graph estimates from existing vector autoregression methods tend to be quite dense and difficult to interpret, unless one compromises on the goodness-of-fit. To address this issue, this paper proposes to incorporate a commonly used structural assumption -- that the ground-truth graph should be largely connected, in the sense that it should only contain at most a few components. We take a Bayesian approach and develop a novel tree-rank prior distribution for the regression coefficients. Specifically, this prior distribution forces the non-zero coefficients to appear only on the union of a few spanning trees. Since each spanning tree connects $p$ nodes with only $(p-1)$ edges, it effectively achieves both high connectivity and high sparsity. We develop a computationally efficient Gibbs sampler that is scalable to large sample size and high dimension. In analyzing test-retest functional magnetic resonance imaging data, our model produces a much more interpretable graph estimate, compared to popular existing approaches. In addition, we show appealing properties of this new method, such as efficient computation, mild stability conditions and posterior consistency.

stat.ME↗

arXiv2023

Statistical Proxy based Mean-Reverting Portfolios with Sparsity and Volatility Constraints

Mean-reverting portfolios with volatility and sparsity constraints are of prime interest to practitioners in finance since they are both profitable and well-diversified, while also managing risk and minimizing transaction costs. Three main measures that serve as statistical proxies to capture the mean-reversion property are predictability, portmanteau criterion, and crossing statistics. If in addition, reasonable volatility and sparsity for the portfolio are desired, a convex quadratic or quartic objective function, subject to nonconvex quadratic and cardinality constraints needs to be minimized. In this paper, we introduce and investigate a comprehensive modeling framework that incorporates all the previous proxies proposed in the literature and develop an effective unifying algorithm that is enabled to obtain a Karush-Kuhn-Tucker (KKT) point under mild regularity conditions. Specifically, we present a tailored penalty decomposition method that approximately solves a sequence of penalized subproblems by a block coordinate descent algorithm. To the best of our knowledge, our proposed algorithm is the first for finding volatile, sparse, and mean-reverting portfolios based on the portmanteau criterion and crossing statistics proxies. Further, we establish that the convergence analysis can be extended to a nonconvex objective function case if the starting penalty parameter is larger than a finite bound and the objective function has a bounded level set. Numerical experiments on the S&P 500 data set demonstrate the efficiency of the proposed algorithm in comparison to a semidefinite relaxation-based approach and suggest that the crossing statistics proxy yields more desirable portfolios.

math.OC↗