arXiv subjects

Aleksandr Aravkin

Publications and source records attributed to Aleksandr Aravkin.

At least 19 recordsLinked to original sources

arXiv2026

A joint optimization approach to identifying sparse dynamics using least squares kernel collocation

We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery strategies for the ODE over a function library combined with techniques from reproducing kernel Hilbert space (RKHS) theory for estimating the state and discretizing the ODE. Our numerical experiments reveal that the proposed strategy leads to significant gains in terms of accuracy, sample efficiency, and robustness to noise, both in terms of learning the equation and estimating the unknown states. This work demonstrates capabilities well beyond existing and widely used algorithms while extending the modeling flexibility of other recent developments in equation discovery.

stat.ME↗

arXiv2025

On-line learning of dynamic systems: sparse regression meets Kalman filtering

Learning governing equations from data is central to understanding the behavior of physical systems across diverse scientific disciplines, including physics, biology, and engineering. The Sindy algorithm has proven effective in leveraging sparsity to identify concise models of nonlinear dynamical systems. In this paper, we extend sparsity-driven approaches to real-time learning by integrating a cornerstone algorithm from control theory -- the Kalman filter (KF). The resulting Sindy Kalman Filter (SKF) unifies both frameworks by treating unknown system parameters as state variables, enabling real-time inference of complex, time-varying nonlinear models unattainable by either method alone. Furthermore, SKF enhances KF parameter identification strategies, particularly via look-ahead error, significantly simplifying the estimation of sparsity levels, variance parameters, and switching instants. We validate SKF on a chaotic Lorenz system with drifting or switching parameters and demonstrate its effectiveness in the real-time identification of a sparse nonlinear aircraft model built from real flight data.

cs.LG↗

arXiv2025

Optimization Outperforms Unscented Techniques for Nonlinear Smoothing

We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can be framed as the Gauss-Newton method for a nonlinear least squares maximum a posteriori loss, and stabilized with standard globalization techniques. We compare the performance of the Optimized Kalman Smoother (OKS) to Unscented Kalman smoothing techniques, and show that they achieve significant improvement for highly nonlinear systems, particularly in noisy settings. The comparison is performed across standard parameter choices (such as the trade-off between process and measurement terms). To our knowledge, this is the first comparison of these methods in the literature.

math.OC↗

arXiv2025

Raking mortality rates across cause, population group and geography with uncertainty quantification

The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) is the single largest and most detailed scientific effort ever conducted to quantify levels and trends in health. This global health model to estimate mortality rates and other health metrics is run at different scales, leading to large data sets of results for a global region and its different sub-regions, or for a cause of death and different sub-causes for example. These models do not necessarily lead to consistent data tables where, for instance, the sum of the number of deaths for each of the sub-regions is equal to the number of deaths for the global region. Raking is widely used in survey inference and global health models to adjust the observations in contingency tables to given marginals, in the latter case reconciling estimates between models with different granularities. The results of global health models usually associate to the point estimates an uncertainty, such as standard deviations or confidence intervals. In this paper, we propose an uncertainty propagation approach that obtains, at the cost of a single solve, nearly the same uncertainty estimates as computationally intensive Monte Carlo techniques that pass thousands of observed and marginal samples through the entire raking process. We introduce a convex optimization approach that provides a unified framework to raking extensions such as uncertainty propagation, raking with differential weights, raking with different loss functions in order to ensure that bounds on estimates are respected, verifying the feasibility of the constraints, raking to margins either as hard constraints or as aggregate observations, and handling missing data.

stat.ME↗

arXiv2024

WENDY: Covariance Dynamics Based Gene Regulatory Network Inference

Determining gene regulatory network (GRN) structure is a central problem in biology, with a variety of inference methods available for different types of data. For a widely prevalent and challenging use case, namely single-cell gene expression data measured after intervention at multiple time points with unknown joint distributions, there is only one known specifically developed method, which does not fully utilize the rich information contained in this data type. We develop an inference method for the GRN in this case, netWork infErence by covariaNce DYnamics, dubbed WENDY. The core idea of WENDY is to model the dynamics of the covariance matrix, and solve this dynamics as an optimization problem to determine the regulatory relationships. To evaluate its effectiveness, we compare WENDY with other inference methods using synthetic data and experimental data. Our results demonstrate that WENDY performs well across different data sets.

q-bio.MN↗

arXiv2024

A Stochastic Record-Value Approach to Global Simulation Optimization

Black-box optimization is ubiquitous in machine learning, operations research and engineering simulation. Black-box optimization algorithms typically do not assume structural information about the objective function and thus must make use of stochastic information to achieve statistical convergence to a globally optimal solution. One such class of methods is multi-start algorithms which use a probabilistic criteria to: determine when to stop a single run of an iterative optimization algorithm, also called an inner search, when to perform a restart, or outer search, and when to terminate the entire algorithm. Zabinsky, Bulger & Khompatraporn introduced a record-value theoretic multi-start framework called Dynamic Multi-start Sequential Search (DMSS). We observe that DMSS performs poorly when the inner search method is a deterministic gradient-based search. In this thesis, we present an algorithmic modification to DMSS and empirically show that the Revised DMSS (RDMSS) algorithm can outperform DMSS in gradient-based settings for a broad class of objective test functions. We give a theoretical analysis of a stochastic process that was constructed specifically as an inner search stopping criteria within RDMSS. We discuss computational considerations of the RDMSS algorithm. Finally, we present numerical results to determine its effectiveness.

math.OC↗

arXiv2024

Corrected Correlation Estimates for Meta-Analysis

Meta-analysis allows rigorous aggregation of estimates and uncertainty across multiple studies. When a given study reports multiple estimates, such as log odds ratios (ORs) or log relative risks (RRs) across exposure groups, accounting for within-study correlations improves accuracy and efficiency of meta-analytic results. Canonical approaches of Greenland-Longnecker and Hamling estimate pseudo cases and non-cases for exposure groups to obtain within-study correlations. However, currently available implementations for both methods fail on simple examples. We review both GL and Hamling methods through the lens of optimization. For ORs, we provide modifications of each approach that ensure convergence for any feasible inputs. For GL, this is achieved through a new connection to entropic minimization. For Hamling, a modification leads to a provably solvable equivalent set of equations given a specific initialization. For each, we provide implementations a guaranteed to work for any feasible input. For RRs, we show the new GL approach is always guaranteed to succeed, but any Hamling approach may fail: we give counter-examples where no solutions exist. We derive a sufficient condition on reported RRs that guarantees success when reported variances are all equal.

stat.ME↗

arXiv2024

Learning Nonlinear Dynamics Using Kalman Smoothing

Identifying Ordinary Differential Equations (ODEs) from measurement data requires both fitting the dynamics and assimilating, either implicitly or explicitly, the measurement data. The Sparse Identification of Nonlinear Dynamics (SINDy) method involves a derivative estimation step (and optionally, smoothing) and a sparse regression step on a library of candidate ODE terms. Kalman smoothing is a classical framework for assimilating the measurement data with known noise statistics. Previously, derivatives in SINDy and its python package, pysindy, had been estimated by finite difference, L1 total variation minimization, or local filters like Savitzky-Golay. In contrast, Kalman allows discovering ODEs that best recreate the essential dynamics in simulation, even in cases when it does not perform as well at recovering coefficients, as measured by their F1 score and mean absolute error. We have incorporated Kalman smoothing, along with hyperparameter optimization, into the existing pysindy architecture, allowing for rapid adoption of the method. Numerical experiments on a number of dynamical systems show Kalman smoothing to be the most amenable to parameter selection and best at preserving problem structure in the presence of noise.

math.DS↗

arXiv2024

Spatiotemporal k-means

Spatiotemporal data is increasingly available due to emerging sensor and data acquisition technologies that track moving objects. Spatiotemporal clustering addresses the need to efficiently discover patterns and trends in moving object behavior without human supervision. One application of interest is the discovery of moving clusters, where clusters have a static identity, but their location and content can change over time. We propose a two phase spatiotemporal clustering method called spatiotemporal k-means (STkM) that is able to analyze the multi-scale relationships within spatiotemporal data. By optimizing an objective function that is unified over space and time, the method can track dynamic clusters at both short and long timescales with minimal parameter tuning and no post-processing. We begin by proposing a theoretical generating model for spatiotemporal data and prove the efficacy of STkM in this setting. We then evaluate STkM on a recently developed collective animal behavior benchmark dataset and show that STkM outperforms baseline methods in the low-data limit, which is a critical regime of consideration in many emerging applications. Finally, we showcase how STkM can be extended to more complex machine learning tasks, particularly unsupervised region of interest detection and tracking in videos.

cs.LG↗

arXiv2024

Robust Nonparametric Stochastic Frontier Analysis

Benchmarking tools, including stochastic frontier analysis (SFA), data envelopment analysis (DEA), and its stochastic extension (StoNED) are core tools in economics used to estimate an efficiency envelope and production inefficiencies from data. The problem appears in a wide range of fields -- for example, in global health the frontier can quantify efficiency of interventions and funding of health initiatives. Despite their wide use, classic benchmarking approaches have key limitations that preclude even wider applicability. Here we propose a robust non-parametric stochastic frontier meta-analysis (SFMA) approach that fills these gaps. First, we use flexible basis splines and shape constraints to model the frontier function, so specifying a functional form of the frontier as in classic SFA is no longer necessary. Second, the user can specify relative errors on input datapoints, enabling population-level analyses. Third, we develop a likelihood-based trimming strategy to robustify the approach to outliers, which otherwise break available benchmarking methods. We provide a custom optimization algorithm for fast and reliable performance. We implement the approach and algorithm in an open source Python package `sfma'. Synthetic and real examples show the new capabilities of the method, and are used to compare SFMA to state of the art benchmarking packages that implement DEA, SFA, and StoNED.

stat.ME↗

arXiv2023

Ensemble Principal Component Analysis

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large, multivariate datasets today. Two well-known limitations of the method include sensitivity to outliers and noise and no clear methodology for the uncertainty quantification of the principle components or their associated explained variances. Whereas previous work has focused on each of these problems individually, we propose a scalable method called Ensemble PCA (EPCA) that addresses them simultaneously for data which has an inherently low-rank structure. EPCA combines boostrapped PCA with k-means cluster analysis to handle challenges associated with sign-ambiguity and the re-ordering of components in the PCA subsamples. EPCA provides a noise-resistant extension of PCA that lends itself naturally to uncertainty quantification. We test EPCA on data corrupted with white noise, sparse noise, and outliers against both classical PCA and Robust PCA (RPCA) and show that EPCA performs competitively across different noise scenarios, with a clear advantage on datasets containing outliers and orders of magnitude reduction in computational cost compared to RPCA.

stat.CO↗

arXiv2023

Deep networks for system identification: a Survey

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden properties of the observations. System identification learns mathematical descriptions of dynamic systems from input-output data and can thus benefit from the advances of deep neural networks to enrich the possible range of models to choose from. For this reason, we provide a survey of deep learning from a system identification perspective. We cover a wide spectrum of topics to enable researchers to understand the methods, providing rigorous practical and theoretical insights into the benefits and challenges of using them. The main aim of the identified model is to predict new data from previous observations. This can be achieved with different deep learning based modelling techniques and we discuss architectures commonly adopted in the literature, like feedforward, convolutional, and recurrent networks. Their parameters have to be estimated from past data trying to optimize the prediction performance. For this purpose, we discuss a specific set of first-order optimization tools that is emerged as efficient. The survey then draws connections to the well-studied area of kernel-based methods. They control the data fit by regularization terms that penalize models not in line with prior assumptions. We illustrate how to cast them in deep architectures to obtain deep kernel-based methods. The success of deep learning also resulted in surprising empirical observations, like the counter-intuitive behaviour of models with many parameters. We discuss the role of overparameterized models, including their connection to kernels, as well as implicit regularization mechanisms which affect generalization, specifically the interesting phenomena of benign overfitting ...

cs.LG↗

arXiv2022

Analysis of Relaxation Methods for Feature Selection in Mixed Effects Models

Linear Mixed-Effects (LME) models are a fundamental tool for modeling clustered data, including cohort studies, longitudinal data analysis, and meta-analysis. The design and analysis of variable selection methods for LMEs is considerably more difficult than for linear regression because LME models are nonlinear. The approach considered here is motivated by a recent method for sparse relaxed regularized regression (SR3) for variable selection in the context of linear regression. The theoretical underpinnings for the proposed extension to LMEs are developed, including consistency results, variational properties, implementability of optimization methods, and convergence results. In particular we provide convergence analyses for a basic implementation of SR3 for LME (called MSR3) and an accelerated hybrid algorithm (called MSR3-fast). Numerical results show the utility and speed of these algorithms on realistic simulated datasets. The numerical implementations are available in an open source python package pysr3.

stat.ME↗

arXiv2022

Theoretical Advances in Current Estimation and Navigation from a Glider-Based Acoustic Doppler Current Profiler (ADCP)

We examine acoustic Doppler current profiler (ADCP) measurements from underwater gliders to determine glider position, glider velocity, and subsurface current. ADCPs, however, do not directly observe the quantities of interest; instead, they measure the relative motion of the vehicle and the water column. We examine the lineage of mathematical innovations that have previously been applied to this problem, discovering an unstated but incorrect assumption of independence. We reframe a recent method to form a joint probability model of current and vehicle navigation, which allows us to correct this assumption and extend the classic Kalman smoothing method. Detailed simulations affirm the efficacy of our approach for computing estimates and their uncertainty. The joint model developed here sets the stage for future work to incorporate constraints, range measurements, and robust statistical modeling.

math.OC↗

arXiv2022

A Relaxation Approach to Feature Selection for Linear Mixed Effects Models

Linear Mixed-Effects (LME) models are a fundamental tool for modeling correlated data, including cohort studies, longitudinal data analysis, and meta-analysis. Design and analysis of variable selection methods for LMEs is more difficult than for linear regression because LME models are nonlinear. In this work we propose a relaxation strategy and optimization methods that enable a wide range of variable selection methods for LMEs using both convex and nonconvex regularizers, including $\ell_1$, Adaptive-$\ell_1$, CAD, and $\ell_0$. The computational framework only requires the proximal operator for each regularizer to be available, and the implementation is available in an open source python package pysr3, consistent with the sklearn standard. The numerical results on simulated data sets indicate that the proposed strategy improves on the state of the art for both accuracy and compute time. The variable selection techniques are also validated on a real example using a data set on bullying victimization.

stat.ME↗

arXiv2021

A hyperparameter-tuning approach to automated inverse planning

Radiotherapy inverse planning often requires planners to modify parameters in the treatment planning system's objective function to produce clinically acceptable plans. Due to the manual steps in this process, plan quality can vary depending on the planning time available and the planner's skills. This study investigates two hyperparameter-tuning methods for automated inverse planning. Because this framework does not train a model on previously-optimized plans, it can be readily adapted to practice pattern changes, and plan quality is not limited by that of a training cohort. We selected 10 patients who received lung SBRT using manually-generated clinical plans. We used random sampling (RS) and Bayesian optimization (BO) to tune parameters using linear-quadratic utility functions based on 11 clinical goals. Normalizing all plans to have PTV D95 equal to 48 Gy, we compared plan quality for the automatically-generated and manually-generated plans. We also investigated the impact of iteration count on the automatically-generated plans, comparing planning time and plan utility for RS and BO plans with and without stopping criteria. Without stopping criteria, the median planning time was 1.9 and 2.3 hours for RS and BO plans. The OAR doses in the RS and BO plans had a median percent difference (MPD) of 48.7% and 60.4% below clinical dose limits and an MPD of 2.8% and 3.3% below clinical plan doses. With stopping criteria, the utility decreased by an MPD of 5.3% and 3.9% for RS and BO plans, but the median planning time was reduced to 0.5 and 0.7 hours, and the OAR doses still had an MPD of 42.9% and 49.7% below clinical dose limits and an MPD of 0.3% and 1.8% below clinical plan doses. This study demonstrates that hyperparameter-tuning approaches to automated inverse planning can reduce active planning time with plan quality that is similar to or better than manually-generated plans.

physics.med-ph↗

arXiv2021

Analysis and Methods to Mitigate Effects of Under-reporting in Count Data

Under-reporting of count data poses a major roadblock for prediction and inference. In this paper, we focus on the Pogit model, which deconvolves the generating Poisson process from the censuring process controlling under-reporting using a generalized linear modeling framework. We highlight the limitations of the Pogit model and address them by adding constraints to the estimation framework. We also develop uncertainty quantification techniques that are robust to model mis-specification. Our approach is evaluated using synthetic data and applied to real healthcare datasets, where we treat in-patient data as `reported' counts and use held-out total injuries to validate the results. The methods make it possible to separate the Poisson process from the under-reporting process, given sufficient expert information. Codes to implement the approach are available via an open source Python package.

stat.ME↗

arXiv2021

Robust Trimmed k-means

Clustering is a fundamental tool in unsupervised learning, used to group objects by distinguishing between similar and dissimilar features of a given data set. One of the most common clustering algorithms is k-means. Unfortunately, when dealing with real-world data many traditional clustering algorithms are compromised by lack of clear separation between groups, noisy observations, and/or outlying data points. Thus, robust statistical algorithms are required for successful data analytics. Current methods that robustify k-means clustering are specialized for either single or multi-membership data, but do not perform competitively in both cases. We propose an extension of the k-means algorithm, which we call Robust Trimmed k-means (RTKM) that simultaneously identifies outliers and clusters points and can be applied to either single- or multi-membership data. We test RTKM on various real-world datasets and show that RTKM performs competitively with other methods on single membership data with outliers and multi-membership data without outliers. We also show that RTKM leverages its relative advantages to outperform other methods on multi-membership data containing outliers.

stat.ML↗