arXiv subjects

Arnab Ganguly

Publications and source records attributed to Arnab Ganguly.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Confidence Intervals via Moderate Deviations Theory

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming problem or various SDE models. More precisely, we develop a systematic construction of highly accurate confidence intervals by using a moderate deviation principle-based approach. It is shown that the proposed confidence intervals are statistically optimal in the sense that they satisfy criteria regarding exponential accuracy, minimality, consistency, mischaracterization probability, and eventual uniformly most accurate (UMA) property. The confidence intervals suggested by this approach are expressed as solutions to robust optimization problems, where the uncertainty is expressed via the underlying moderate deviation rate function induced by the data-generating process. We demonstrate that for many models these optimization problems admit tractable reformulations as finite convex programs even when they are infinite-dimensional.

stat.ML↗

arXiv2026

Spintronic Neuromorphic Hardware Using Domain Wall-Based Neurons and Quantized Synapses

In this work, we simulate the functionality of an artificial neuron and synapse using spin-orbit torque-based spintronic devices and implement a fully connected artificial neural network (ANN). These neuro-synaptic devices are emulated via transverse domain wall dynamics within a rectangular magnetic nanotrack comprised of heavy-metal (HM)/ferromagnet (FM) heterostructures. Here, the heterostructure is parameterized using Pt-based alloys for the HM layer and CoFeB for the FM layer. The ReLU activation function of the neuron has been mimicked using the domain wall (DW) motion induced by a 3 ns current pulse. The synapse is modeled using current-induced DW dynamics with a corrugated HM/FM nanotrack. Semicircular notches are symmetrically positioned along both edges of the nanotrack to serve as pinning sites. By applying 10 ns current pulses of varying current densities, we achieve controlled, stepwise DW motion characterized by temporary pauses at consecutive pinning centers. The electrical conductance of the pinned DW across various pinning points act as stable synaptic weights for our ANN. Furthermore, we observe a threshold-dependent delay effect where each depinning event is influenced by previous ones, successfully mimicking synaptic states and adaptability in neuromorphic systems. The fully connected ANN has been modeled using the conventional float32 synaptic weights for the MNIST and Fashion-MNIST datasets with an accuracy of ~97% and ~86%, respectively, which serves as a test bed for our neuromorphic simulations. To implement a sparse and low-memory-footprint ANN, we quantize the trained synaptic weights into discrete quantized levels and tested the network, which demonstrate an accuracy of ~95% and ~62% for the MNIST and Fashion-MNIST datasets, respectively.

cond-mat.mes-hall↗

arXiv2026

Learning stochastic multiscale models through normalizing flows

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a single trajectory of the slow component, while the fast dynamics remain unobserved, making statistical learning challenging. Approaches based on partial differential equations (PDE), such as Fokker-Planck formulations, aim to characterize the evolution of probability densities, typically requiring dense space-time data or grid-based solvers. In contrast, we adopt a trajectory-based perspective and develop a data-driven framework for learning effective stochastic dynamics from a single observed path. We model the dynamics by coupled multiscale stochastic differential equations (SDEs) and first obtain a principled model reduction through stochastic averaging. Unlike generic model reduction techniques such as PCA, this respects the dynamical structure of the original system and explicitly incorporates the interaction between slow and fast scales. A central challenge, however, is that the reduced model depends on the invariant distribution of the fast process, which is a solution to an intractable and often unknown PDE. We introduce a novel learning framework that parameterizes the invariant distribution using normalizing flows, enabling expressive density modeling in the latent fast-variable space. The flow is trained end-to-end by optimizing a penalized likelihood objective induced by the reduced stochastic dynamics. Furthermore, we develop a Bayesian variational inference procedure for uncertainty quantification, employing a second normalizing flow to approximate the posterior distribution over model parameters. This yields a scalable approach to capturing epistemic uncertainty in multiscale systems.

stat.ML↗

arXiv2026

Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and parameters from sparse, noisy observations. Classical smoothing methods for this problem are often limited by path degeneracy and poor scalability. In this work, we developed a novel method based on characterization of the posterior SDE in terms of conditional backward-in-time score defined as the gradient of a function solving a Kolmogorov backward equation with multiplicative updates at observation times. We learn this conditional score using neural networks trained to satisfy both the governing PDE and the observation-induced jump conditions, thereby integrating continuous-time dynamics with discrete Bayesian updates. The resulting score induces a posterior SDE with the same diffusion coefficient but a modified drift, enabling efficient posterior trajectory sampling. We further derive a likelihood-based objective for learning the SDE parameters, yielding an evidence lower bound (ELBO) for joint state smoothing and parameter estimation. This leads to a variational EM-style procedure, where the neural conditional score is optimized to approximate the smoothing distribution, followed by a maximization step over the SDE parameters using samples from the induced posterior. Experiments on nonlinear systems demonstrate accurate and stable inference with a very few observations demonstrating significant improved scalability compared to classical MCMC methods.

stat.ML↗

arXiv2026

Statistical inference for a multiscale stochastic model of enzyme kinetics via propagation of chaos

We study a class of Stochastic Differential Equations (SDEs) with jumps modeling multistage Michaelis--Menten enzyme kinetics, in which a substrate is sequentially transformed into a product via a cascade of intermediate complexes. These networks are typically high-dimensional and exhibit multiscale behavior with a strong coupling between different components, posing substantial analytical and computational challenges. In particular, the problem of statistical inference of reaction rates is significantly difficult and becomes even more intricate when direct observations of system states are unavailable and only a random sample of product formation times is observed. We address this problem in two stages. First, in a suitable scaling regime consistent with the Quasi-Steady State Approximation (QSSA), we rigorously establish a stochastic averaging principle yielding a reduced model for the product-substrate dynamics. Guided by the reduced-order dynamics, we next construct a novel Interacting Particle System (IPS) that approximates the product-substrate process at the particle level. This IPS plays a pivotal role in the inference methodology, and we prove several non-asymptotic bounds and limiting results for this system. These results facilitate the construction of an estimator based on a product-form approximate likelihood requiring only a random sample of product formation times. This approach does not need access to the system states, and we rigorously prove consistency of the estimator.

math.PR↗

arXiv2026

Stochastic Averaging and Statistical Inference of Glycolytic Pathway

Many biological processes exhibit oscillatory behavior. Among these, glycolytic oscillations have been extensively studied due to their well-characterized biochemical reaction networks. However, the complexity of these networks necessitates low-dimensional ordinary differential equation (ODE) models to identify core mechanisms and perform stability analysis. While previous studies proposed reduced ODE models, these were typically introduced from deterministic descriptions rather than the underlying stochastic dynamics, which more accurately represent discrete reaction events occurring at random times. In this paper, we develop a rigorous probabilistic framework for deriving a reduced Othmer-Aldridge model of the glycolytic pathway from its stochastic formulation. The full system is modeled as a multiscale continuous-time Markov chain with different time and abundance scales. Under an appropriate scaling regime and specific structural conditions, we prove that the dynamics of the slow components are approximated by a two-dimensional ODE. The proof is technically involved due to the network's complexity and strong coupling between its components. We further consider the problem of parameter estimation when observations are limited to the slow species: fructose-6-phosphate and ADP. The reduced system yields a tractable loss function depending solely on these variables. We prove that the resulting estimators are statistically consistent when the data originate from the full stochastic reaction network. Together, these results provide a mathematically rigorous framework linking stochastic biochemical reaction networks, reduced deterministic dynamics, and statistically reliable parameter estimation.

math.PR↗

arXiv2025

Asymptotic Analysis of the Total Quasi-Steady State Approximation for the Michaelis--Menten Enzyme Kinetic Reactions

We consider a stochastic model of the Michaelis-Menten (MM) enzyme kinetic reactions in terms of Stochastic Differential Equations (SDEs) driven by Poisson Random Measures (PRMs). It has been argued that among various Quasi-Steady State Approximations (QSSAs) for the deterministic model of such chemical reactions, the total QSSA (tQSSA) is the most accurate approximation, and it is valid for a wider range of parameter values than the standard QSSA (sQSSA). While the sQSSA for this model has been rigorously derived from a probabilistic perspective at least as early as 2006 in Ball et al. (2006), a rigorous study of the tQSSA for the stochastic model appears missing. We fill in this gap by deriving it as a Functional Law of Large Numbers (FLLN), and also studying the fluctuations around this approximation as a Functional Central Limit Theorem (FCLT).

math.PR↗

arXiv2025

Nonparametric learning of stochastic differential equations from sparse and noisy data

The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift, our goal here is to learn the entire drift function directly from data without strong structural assumptions, making it especially relevant in scientific disciplines where system dynamics are partially understood or highly complex. We cast the estimation problem as minimization of the penalized negative log-likelihood functional over a reproducing kernel Hilbert space (RKHS). In the sparse observation regime, the presence of unobserved trajectory segments makes the SDE likelihood intractable. To address this, we develop an Expectation-Maximization (EM) algorithm that employs a novel Sequential Monte Carlo (SMC) method to approximate the filtering distribution and generate Monte Carlo estimates of the E-step objective. The M-step then reduces to a penalized empirical risk minimization problem in the RKHS, whose minimizer is given by a finite linear combination of kernel functions via a generalized representer theorem. To control model complexity across EM iterations, we also develop a hybrid Bayesian variant of the algorithm that uses shrinkage priors to identify significant coefficients in the kernel expansion. We establish important theoretical convergence results for both the exact and approximate EM sequences. The resulting EM-SMC-RKHS procedure enables accurate estimation of the drift function of stochastic dynamical systems in low-data regimes and is broadly applicable across domains requiring continuous-time modeling under observational constraints. We demonstrate the effectiveness of our method through a series of numerical experiments.

stat.ML↗

arXiv2025

Nonparametric learning of covariate-based Markov jump processes using RKHS techniques

We propose a novel nonparametric approach for linking covariates to Continuous Time Markov Chains (CTMCs) using the mathematical framework of Reproducing Kernel Hilbert Spaces (RKHS). CTMCs provide a robust framework for modeling transitions across clinical or behavioral states, but traditional multistate models often rely on linear relationships. In contrast, we use a generalized Representer Theorem to enable tractable inference in functional space. For the Frequentist version, we apply normed square penalties, while for the Bayesian version, we explore sparsity inducing spike and slab priors. Due to the computational challenges posed by high-dimensional spaces, we successfully adapt the Expectation Maximization Variable Selection (EMVS) algorithm to efficiently identify the posterior mode. We demonstrate the effectiveness of our method through extensive simulation studies and an application to follicular cell lymphoma data. Our performance metrics include the normalized difference between estimated and true nonlinear transition functions, as well as the difference in the probability of getting absorbed in one the final states, capturing the ability of our approach to predict long-term behaviors.

stat.ME↗

arXiv2024

Asymptotic analysis of estimators of ergodic stochastic differential equations

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of the diffusion parameter and an approximate maximum likelihood estimator of the drift parameter based on a discretized likelihood function have been established in a suitable scaling regime involving the time-gap between the observations and the overall time span. Our framework is more general than that typically considered in the literature and, thus, has the potential to be applicable to a wider range of stochastic models.

math.ST↗

arXiv2023

Controlling the Skyrmion Density and Size for Quantized Convolutional Neural Networks

Skyrmion devices show energy efficient and high integration data storage and computing capabilities. Herein, we present the results of experimental and micromagnetic investigations of the creation and stability of magnetic skyrmions in the Ta/IrMn/CoFeB/MgO thin film system. We investigate the magnetic-field dependence of the skyrmion density and size using polar magneto optical Kerr effect MOKE microscopy supported by a micromagnetic study. The evolution of the topological charge with time under a magnetic field is investigated, and the transformation dynamics are explained. Furthermore, considering the voltage control of these skyrmion devices, we evaluate the dependence of the skyrmion size and density on the Dzyaloshinskii Moriya interaction and the magnetic anisotropy. We furthermore propose a skyrmion based synaptic device based on the results of the MOKE and micromagnetic investigations. We demonstrate the spin-orbit torque controlled discrete topological resistance states with high linearity and uniformity in the device. The discrete nature of the topological resistance makes it a good candidate to realize hardware implementation of weight quantization in a quantized neural network (QNN). The neural network is trained and tested on the CIFAR10 dataset, where the devices act as synapses to achieve a recognition accuracy of 87%, which is comparable to the result of ideal software-based methods.

cond-mat.mtrl-sci↗

arXiv2022

Moment stability of stochastic processes with applications to control systems

We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the sizes of the one-step jumps of the processes. The state-dependent feature of the results make them suitable for a large class of multiplicative-noise processes. Under the additional assumption of Markovian property, new result on ergodicity has also been proved. There are several applications to iterative systems, control systems, and other dynamical systems with state-dependent multiplicative noise, and we include illustrative examples to demonstrate applicability of our results.

math.PR↗

arXiv2022

Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations

The paper has two major themes. The first part of the paper establishes certain general results for infinite-dimensional optimization problems on Hilbert spaces. These results cover the classical representer theorem and many of its variants as special cases and offer a wider scope of applications. The second part of the paper then develops a systematic approach for learning the drift function of a stochastic differential equation by integrating the results of the first part with Bayesian hierarchical framework. Importantly, our Baysian approach incorporates low-cost sparse learning through proper use of shrinkage priors while allowing proper quantification of uncertainty through posterior distributions. Several examples at the end illustrate the accuracy of our learning scheme.

stat.ML↗

arXiv2022

Skyrmion-Magnetic Tunnel Junction Synapse with Mixed Synaptic Plasticity for Neuromorphic Computing

Magnetic skyrmion-based data storage and unconventional computing devices have gained increasing attention due to their topological protection, small size, and low driving current. However, skyrmion creation, deletion, and motion are still being studied. In this study, we propose a skyrmion-based neuromorphic magnetic tunnel junction (MTJ) device with both long- and short-term plasticity (LTP and STP) (mixed synaptic plasticity). We showed that plasticity could be controlled by magnetic field, spin-orbit torque (SOT), and the voltage-controlled magnetic anisotropy (VCMA) switching mechanism. LTP depends on the skyrmion density and is manipulated by the SOT and magnetic field while STP is controlled by the VCMA. The LTP property of the device was utilized for static image recognition. By incorporating the STP feature, the device gained additional temporal filtering ability and could adapt to a dynamic environment. The skyrmions were conserved and confined to a nanotrack to minimize the skyrmion nucleation energy. The synapse device was trained and tested for emulating a deep neural network. We observed that when the skyrmion density was increased, the inference accuracy improved: 90% accuracy was achieved by the system at the highest density. We further demonstrated the dynamic environment learning and inference capabilities of the proposed device.

cond-mat.mtrl-sci↗

arXiv2020

Context-Aware Design of Cyber-Physical Human Systems (CPHS)

Recently, it has been widely accepted by the research community that interactions between humans and cyber-physical infrastructures have played a significant role in determining the performance of the latter. The existing paradigm for designing cyber-physical systems for optimal performance focuses on developing models based on historical data. The impacts of context factors driving human system interaction are challenging and are difficult to capture and replicate in existing design models. As a result, many existing models do not or only partially address those context factors of a new design owing to the lack of capabilities to capture the context factors. This limitation in many existing models often causes performance gaps between predicted and measured results. We envision a new design environment, a cyber-physical human system (CPHS) where decision-making processes for physical infrastructures under design are intelligently connected to distributed resources over cyberinfrastructure such as experiments on design features and empirical evidence from operations of existing instances. The framework combines existing design models with context-aware design-specific data involving human-infrastructure interactions in new designs, using a machine learning approach to create augmented design models with improved predictive powers.

cs.AI↗

arXiv2018

Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Error analysis through central limit theorem and moderate deviation asymptotics

The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a thorough error analysis is conducted by proving central limit theorem and moderate deviation principle for the error term. The paper is a first step in understanding efficiency of discretization based numerical schemes for estimating invariant distributions, which is comparatively much less studied than the schemes used for generating approximate trajectories of diffusions over finite time intervals. The potential applications of these results also extend to other areas including mathematical physics, parameter inference of ergodic diffusions and analysis of multiscale dynamical systems with averaging.

math.PR↗

arXiv2017

Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales

The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of semimartingales considered is broad enough to cover Banach space-valued semimartingales and the martingale random measures. Simple usable expressions for the associated rate functions are given in this abstract setup. As illustrated through several concrete examples, the results presented here provide a new systematic approach to the study of large deviation principles for a sequence of Markov processes. Keywords: large deviations, stochastic integration, stochastic differential equations, exponential tightness, Markov processes, infinite dimensional semimartingales, Banach space-valued semimartingales

math.PR↗

arXiv2017

Large Deviations for Small Noise Diffusions in a Fast Markovian Environment

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional Itô stochastic differential equation, and the fast component is a finite state pure jump process. Previous works have considered settings where the coupling between the components is weak in a certain sense. In the current work we study a fully coupled system in which the drift and diffusion coefficient of the slow component and the jump intensity function and jump distribution of the fast process depend on the states of both components. In addition, the diffusion can be degenerate. Our proofs use certain stochastic control representations for expectations of exponential functionals of finite dimensional Brownian motions and Poisson random measures together with weak convergence arguments. A key challenge is in the proof of the large deviation lower bound where, due to the interplay between the degeneracy of the diffusion and the full dependence of the coefficients on the two components, the associated local rate function has poor regularity properties.

math.PR↗