arXiv subjects

Alokesh Manna

Publications and source records attributed to Alokesh Manna.

8 recordsLinked to original sources

arXiv2026

Bigraphical Matérn-Whittle (BMW) Processes for Fast Inference of Big Multivariate Spatial Data on General Domains

Large spatial data sets now record many correlated variables at many thousands of locations, often on domains where Euclidean distance misrepresents proximity. The central difficulty is modelling the cross-variable dependence jointly while retaining variable-level interpretation. We introduce the bigraphical Mat'ern-Whittle process, a multivariate Gaussian process that resolves this with two graphs. A spatial graph generates the Mat'ern structure of each variable through a fractional power of a graph Laplacian, so the process is valid on any topology, with per-variable range, smoothness and amplitude. A directed acyclic variable graph encodes the scientific structure: we prove that each absent edge yields an exact conditional independence between the corresponding fields. We further prove that the operator determinant does not involve the cross-dependence coefficients, which keeps matrix-free likelihood evaluation and Bayesian learning of the variable graph tractable at scale. Estimation requires only sparse matrix-vector products and scales to tens of millions of space-variable pairs. In simulations the method recovered parameters and graphs accurately, remained robust under misspecification, and halved held-out prediction error on a non-convex domain. In a spatial transcriptomics section with 19,809 cells and 1,122 genes, fitted in 75 minutes on a laptop, borrowing across the learned gene graph reduced held-out prediction error by 50 to 91 percent. Theoretical challenges, such as the achievable efficiency of estimating the variance of the nugget, are also explored.

stat.ME↗

arXiv2026

Scalable spatial point process models for forensic footwear analysis

Shoe print evidence recovered from crime scenes plays a key role in forensic investigations. By examining shoe prints, investigators can determine details of the footwear worn by suspects. However, establishing that a suspect's shoes match the make and model of a crime scene print may not be sufficient. Typically, thousands of shoes of the same size, make, and model are manufactured, any of which could be responsible for the print. Accordingly, a popular approach used by investigators is to examine the print for signs of ``accidentals,'' i.e., cuts, scrapes, and other features that accumulate on shoe soles after purchase due to wear. While some patterns of accidentals are common on certain types of shoes, others are highly distinctive, potentially distinguishing the suspect's shoe from all others. Quantifying the rarity of a pattern is thus essential to accurately measuring the strength of forensic evidence. In this study, we address this task by developing a hierarchical Bayesian model. Our improvement over existing methods primarily stems from two advancements. First, we frame our approach in terms of a latent Gaussian model, thus enabling inference to be efficiently scaled to large collections of annotated shoe prints via integrated nested Laplace approximations. Second, we incorporate spatially varying coefficients to model the relationship between shoes' tread patterns and accidental locations. We demonstrate these improvements through superior performance on held-out data, which enhances accuracy and reliability in forensic shoe print analysis.

cs.CV↗

arXiv2026

How Large Language Models Get Stuck: Early structure with persistent errors

Linguistic insights may help make Large Language Model (LLM) training more efficient. We trained Meta's OPT model on the 100M word BabyLM dataset, and evaluated it on the BLiMP benchmark, which consists of 67 classes, each defined by sentence pairs that differ in a targeted syntactic or semantic rule violation. We tested the model's preference for grammatical over ungrammatical sentences across training iterations and grammatical types. In nearly one-third of the BLiMP classes, OPT fails to consistently assign a higher likelihood to grammatical sentences, even after extensive training. When it fails, it often establishes a clear (erroneous) separation of the likelihoods at an early stage of processing and sustains this to the end of our training phase. We hypothesize that this mis-categorization is costly because it creates entrenched biases that must, eventually, be reversed in order for the model to perform well. We probe this phenomenon using a mixture of qualitative (based on linguistic theory and the theory of Deep Learning) and quantitative (based on numerical testing) assessments. Our qualitative assessments indicate that only some BLiMP tests are meaningful guides. We conclude by articulating a hypothesis, the Bigram Hypothesis, which claims that the learning process will exhibit erroneous entrenchment if bigram statistics bias the model toward wrong distinctions early in training, and we describe a method of testing the hypothesis on appropriately selected BLiMP classes.

cs.CL↗

arXiv2025

Bayesian Models for Joint Selection of Features and Auto-Regressive Lags: Theory and Applications in Environmental and Financial Forecasting

We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on contemporaneous or past explanatory variables and persistent stochastic shocks, including financial modeling, hydrological forecasting, and meteorological applications requiring temporal dependency capture. Our methodology uses hierarchical Bayesian models with spike-and-slab priors to simultaneously select relevant covariates and lagged error terms. We propose an efficient two-stage MCMC algorithm separating sampling of variable inclusion indicators and model parameters to address high-dimensional computational challenges. Theoretical analysis establishes posterior selection consistency under mild conditions, even when candidate predictors grow exponentially with sample size, common in modern time series with many potential lagged variables. Through simulations and real applications (groundwater depth prediction, S&P 500 log returns modeling), we demonstrate substantial gains in variable selection accuracy and predictive performance. Compared to existing methods, our framework achieves lower MSPE, improved true model component identification, and greater robustness with autocorrelated noise, underscoring practical utility for model interpretation and forecasting in autoregressive settings.

stat.ME↗

arXiv2025

Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data

The Tweedie exponential dispersion family is a popular choice among many to model insurance losses that consist of zero-inflated semicontinuous data. In such data, it is often important to obtain credibility (inference) of the most important features that describe the endogenous variables. Post-selection inference is the standard procedure in statistics to obtain confidence intervals of model parameters after performing a feature extraction procedure. For a linear model, the lasso estimate often has non-negligible estimation bias for large coefficients corresponding to exogenous variables. To have valid inference on those coefficients, it is necessary to correct the bias of the lasso estimate. Traditional statistical methods, such as hypothesis testing or standard confidence interval construction might lead to incorrect conclusions during post-selection, as they are generally too optimistic. Here we discuss a few methodologies for constructing confidence intervals of the coefficients after feature selection in the Generalized Linear Model (GLM) family with application to insurance data.

stat.ME↗

arXiv2025

Distribution-free inference for LightGBM and GLM with Tweedie loss

Prediction uncertainty quantification is a key research topic in recent years scientific and business problems. In insurance industries (\cite{parodi2023pricing}), assessing the range of possible claim costs for individual drivers improves premium pricing accuracy. It also enables insurers to manage risk more effectively by accounting for uncertainty in accident likelihood and severity. In the presence of covariates, a variety of regression-type models are often used for modeling insurance claims, ranging from relatively simple generalized linear models (GLMs) to regularized GLMs to gradient boosting models (GBMs). Conformal predictive inference has arisen as a popular distribution-free approach for quantifying predictive uncertainty under relatively weak assumptions of exchangeability, and has been well studied under the classic linear regression setting. In this work, we propose new non-conformity measures for GLMs and GBMs with GLM-type loss. Using regularized Tweedie GLM regression and LightGBM with Tweedie loss, we demonstrate conformal prediction performance with these non-conformity measures in insurance claims data. Our simulation results favor the use of locally weighted Pearson residuals for LightGBM over other methods considered, as the resulting intervals maintained the nominal coverage with the smallest average width.

stat.ML↗

arXiv2024

Development of a Statistical Predictive Model for Daily Water Table Depth and Important Variables Selection for Inference

Accurately predicting water table dynamics is vital for sustaining groundwater resources that support ecological functions and anthropogenic activities. This study evaluates a statistical model (BigVAR) that handles three major flexibilities: (a) prediction under a sparsity assumption in coefficients, (b) consideration of a time series autoregression framework, and (c) allowance for lags in both dependent and independent variables for estimating water table depth using daily hydroclimatic data from the USDA Forest Service Santee Experimental Forest (SC) and a site in NC. Data from 2006--2019 (SC) and 1988--2008 (NC) were used, with key predictors including soil and air temperature, precipitation, wind, and radiation. For WS80, RMSE during the dormant season was 10.09 cm, with a daily testing phase RMSE of 14.94 cm. The model achieved an R^2 of 0.93 for 2019 (a dry year) and 0.96 for 2016 (a wet year). Solar radiation, rainfall, and wind direction were among the most influential variables. This predictive model aids in managing wetland hydrology and supports decision-making for forest managers and hydrologists.

stat.AP↗

arXiv2021

Some Clustering-based Change-point Detection Methods Applicable to High Dimension, Low Sample Size Data

Detection of change-points in a sequence of high-dimensional observations is a very challenging problem, and this becomes even more challenging when the sample size (i.e., the sequence length) is small. In this article, we propose some change-point detection methods based on clustering, which can be conveniently used in such high dimension, low sample size situations. First, we consider the single change-point problem. Using k-means clustering based on some suitable dissimilarity measures, we propose some methods for testing the existence of a change-point and estimating its location. High-dimensional behavior of these proposed methods are investigated under appropriate regularity conditions. Next, we extend our methods for detection of multiple change-points. We carry out extensive numerical studies to compare the performance of our proposed methods with some state-of-the-art methods.

stat.ME↗