arXiv subjects

Arash Pourhabib

Publications and source records attributed to Arash Pourhabib.

7 recordsLinked to original sources

arXiv2026

Robust Active Learning for Few-Shot Example Selection in Text-to-SQL

Few-shot example retrieval is the dominant paradigm for grounding large language models (LLMs) in domain-specific text-to-SQL systems. However, the quality of the annotated example bank directly governs system accuracy, and expert annotation is prohibitively expensive. We formalize the active selection of these examples as a constrained experimental design problem over the intrinsic, low-dimensional manifold of semantic query embeddings. Unlike standard active learning frameworks, our setting introduces three critical challenges: varying, query-dependent annotation reliability (heteroscedasticity), strict requirements for spatial diversity across semantic topics (partition matroid constraints), and the inherent reality that the true covariance structure of the embedding space is unknown (misspecification). To address these, we propose a stratified greedy algorithm that maximizes a heteroscedastic mutual information objective. We prove that this objective remains submodular and approximately monotonic on the intrinsic manifold, yielding a theoretical constant-factor approximation guarantee. We establish a spectral bound demonstrating that this approximation guarantee degrades gracefully, rather than catastrophically, when the assumed surrogate kernel diverges from the true underlying data-generating process. Empirical results demonstrate that the proposed strategy significantly reduces labeling effort while maintaining high text-to-SQL retrieval accuracy.

stat.ML↗

arXiv2021

A Reproducing Kernel Hilbert Space Approach to Functional Calibration of Computer Models

This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of functional calibration is motivated by engineering applications where using a constant calibration parameter results in a significant mismatch between outputs from the computer model and the physical experiment. Reproducing kernel Hilbert spaces (RKHS) are used to model the optimal calibration function, defined as the functional relationship between the calibration parameter and control variables that gives the best prediction. This optimal calibration function is estimated through penalized least squares with an RKHS-norm penalty and using physical data. An uncertainty quantification procedure is also developed for such estimates. Theoretical guarantees of the proposed method are provided in terms of prediction consistency and consistency of estimating the optimal calibration function. The proposed method is tested using both real and synthetic data and exhibits more robust performance in prediction and uncertainty quantification than the existing parametric functional calibration method and a state-of-art Bayesian method.

stat.ME↗

arXiv2020

A Bayesian framework for functional calibration of expensive computational models through non-isometric matching

We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of the input variables. A major challenge in many applications is that computational models are expensive and can only be evaluated a limited number of times. Furthermore, without making strong assumptions, the calibration variables are not identifiable. We propose Bayesian non-isometric matching calibration (BNMC) that allows calibration of expensive computational models with only a limited number of samples taken from a computational model and its associated physical system. BNMC replaces the computational model with a dynamic Gaussian process (GP) whose parameters are trained in the calibration procedure. To resolve the identifiability issue, we present the calibration problem from a geometric perspective of non-isometric curve to surface matching, which enables us to take advantage of combinatorial optimization techniques to extract necessary information for constructing prior distributions. Our numerical experiments demonstrate that in terms of prediction accuracy BNMC outperforms, or is comparable to, other existing calibration frameworks.

stat.ML↗

arXiv2019

Sparse Pseudo-input Local Kriging for Large Spatial Datasets with Exogenous Variables

We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers of observations present makes it inefficient to apply full Kriging. In order to reduce computational complexity, this paper proposes Sparse Pseudo-input Local Kriging (SPLK), which utilizes hyperplanes to partition a domain into smaller subdomains and then applies a sparse approximation of the full Kriging to each subdomain. We also develop an optimization procedure to find the desired hyperplanes. To alleviate the problem of discontinuity in the global predictor, we impose continuity constraints on the boundaries of the neighboring subdomains. Furthermore, partitioning the domain into smaller subdomains makes it possible to use different parameter values for the covariance function in each region and, therefore, the heterogeneity in the data structure can be effectively captured. Numerical experiments demonstrate that SPLK outperforms, or is comparable to, the algorithms commonly applied to spatial datasets.

stat.ML↗

arXiv2018

Self-tuned mirror descent schemes for smooth and nonsmooth high-dimensional stochastic optimization

We consider randomized block coordinate stochastic mirror descent (RBSMD) methods for solving high-dimensional stochastic optimization problems with strongly convex objective functions. Our goal is to develop RBSMD schemes that achieve a rate of convergence with a minimum constant factor with respect to the choice of the stepsize sequence. To this end, we consider both subgradient and gradient RBSMD methods addressing nonsmooth and smooth problems, respectively. For each scheme, (i) we develop self-tuned stepsize rules characterized in terms of problem parameters and algorithm settings; (ii) we show that the non-averaging iterate generated by the underlying RBSMD method converges to the optimal solution both in an almost sure and a mean sense; (iii) we show that the mean squared error is minimized. When problem parameters are unknown, we develop a unifying self-tuned update rule that can be applied in both subgradient and gradient SMD methods, and show that for any arbitrary and small enough initial stepsize, a suitably defined error bound is minimized. We provide constant factor comparisons with standard SMD and RBSMD methods. Our numerical experiments performed on an SVM model display that the self-tuned schemes are significantly robust with respect to the choice of problem parameters, and the initial stepsize.

math.OC↗

arXiv2016

Empirical Similarity for Absent Data Generation in Imbalanced Classification

When the training data in a two-class classification problem is overwhelmed by one class, most classification techniques fail to correctly identify the data points belonging to the underrepresented class. We propose Similarity-based Imbalanced Classification (SBIC) that learns patterns in the training data based on an empirical similarity function. To take the imbalanced structure of the training data into account, SBIC utilizes the concept of absent data, i.e. data from the minority class which can help better find the boundary between the two classes. SBIC simultaneously optimizes the weights of the empirical similarity function and finds the locations of absent data points. As such, SBIC uses an embedded mechanism for synthetic data generation which does not modify the training dataset, but alters the algorithm to suit imbalanced datasets. Therefore, SBIC uses the ideas of both major schools of thoughts in imbalanced classification: Like cost-sensitive approaches SBIC operates on an algorithm level to handle imbalanced structures; and similar to synthetic data generation approaches, it utilizes the properties of unobserved data points from the minority class. The application of SBIC to imbalanced datasets suggests it is comparable to, and in some cases outperforms, other commonly used classification techniques for imbalanced datasets.

stat.ML↗

arXiv2016

Sequential Monte Carlo Filtering Estimation of Ebola Progression in West Africa

We use a multivariate formulation of sequential Monte Carlo filter that utilizes mechanistic models for Ebola virus propagation and available incidence data to simultaneously estimate the disease progression states and the model parameters. This method has the advantage of performing the inference online as the new data becomes available and estimates the evolution of basic reproductive ratio $R_0(t)$ of the Ebola outbreak through time. Our analysis identifies a peak in the basic reproductive ratio close to the time when Ebola cases were reported in Europe and the USA.

stat.AP↗