Sharp Minimax Regret for Infinite-Memory Logistic Prediction

We study online prediction for a specific finite-alphabet, exogenously driven source with infinite input memory. Independent Rademacher inputs $(U_t)$ are observed sequentially, and the next binary mark has logit $\sum_{j=1}^{t}θ_jU_{t+1-j}$, where $\abs{θ_j}\leq r_j$ and $\sum_jr_j\leq B$. Regret is expected cumulative excess log loss. Lag $j$ can affect prediction by scale $r_j$ and enters only $n_{T,j}=T-j+1$ prediction rounds, leading to the lag-resolved spectrum $Γ_T(r)=\sum_{j=1}^{T}\log\!\left(1+n_{T,j}r_j^2\right)$. For every summable envelope, a localized Bayesian mixture proves $\cR_T(r)\leq CΓ_T(r)$. For exponential and polynomial envelopes, under the stated finite-sample dimension condition, a Toeplitz-design converse proves $\cR_T(r)\geq cΓ_T(r)$, with constants allowed to depend on the fixed decay parameters and the logit bound. Thus $Γ_T(r)$ is the minimax cumulative-regret scale for this source class in these canonical regimes, giving $Θ(α^{-1}\log^2T)$ for $r_j=Ae^{-αj}$ and $Θ(T^{1/(2s)})$ for $r_j=Aj^{-s}$, $s>1$. The converse is specific to the exogenous lagged model and is not a profile-only theorem for arbitrary stationary infinite-memory sources. Retaining only the most recent $h$ inputs costs order $\sum_{j>h}n_{T,j}θ_j^2$, yet the same worst-case truncation profile can correspond to polynomially different regret. A scaled online Newton predictor attains the spectrum upper bound.

Quality Inspection of Printed Circuit Board Pin Insertion via Semantic Segmentation and Board-Level Feature Extraction

Quality control during printed circuit board (PCB) assembly is a critical step in ensuring reliable electronic products. Detecting misaligned pins during or after pin insertion remains a particularly challenging inspection task. This paper presents an automated defect detection method for identifying incorrectly inserted pins on PCBs. The proposed pipeline combines semantic segmentation using a U-Net architecture with contour-based feature extraction and logistic regression for board-level pass/fail classification. Segmentation masks are used to derive contour representations of individual pins, from which board-level features -such as average contour size- are extracted and used to train a logistic regression classifier. We evaluate the method on two datasets: an industrial collection of real-world PCB images, and a publicly available PCB pin-inspection dataset with substantially different visual characteristics. To assess the effectiveness of the proposed approach, a comparison against PatchCore, an anomaly detection technique new to be applied to pin inspection, as well as instance segmentation-based pin detection is made. The developed method achieved Area Under the Receiver Operating Characteristic Curve (ROC-AUC) values of 0.990 on a random test set split from the industrial data and 1.000 on the public dataset indicating strong separation between pass and fail boards. The results indicate that the proposed approach is a promising candidate for automated pin inspection in industrial environments and achieves strong performance on datasets with substantially different visual characteristics after dataset-specific training.

EDGE: a closed-form directed test for the calibration of probabilistic binary classifiers

A probabilistic binary classifier is judged almost everywhere by discrimination - accuracy, the ROC curve, the area under it. Every such criterion is invariant to a monotone distortion of the predicted probabilities, so a classifier can rank perfectly and still return probabilities that are badly wrong. Calibration is the property decisions need, and the field's instrument for it, the binned expected calibration error with its reliability diagram, is descriptive: it has no null distribution, so it cannot say whether the miscalibration it displays is real or noise, and it depends on the binning. We propose EDGE, a calibration test for the canonical probabilistic classifier, logistic regression. EDGE reads the same binned predicted-versus-observed table a reliability diagram plots, and projects its standardized bin residuals onto a small pre-specified basis of smooth calibration-distortion shapes. Its null distribution is a weighted sum of chi-square variables in closed form, costing one pass over the data and one small eigendecomposition: no refit, no resampling, no tuning, so it can run inside cross-validation loops. Binning also makes it robust to the sparsity continuous features create. Across link and feature misspecification the pre-specified default led or tied every rival binned test on the fitted index in 19 of 22 detectable scenarios, and stayed computable where the refit-based Stukel score test separates in 20% to 28% of sparse samples. Its honest limit is rough, high-frequency miscalibration, where omnibus statistics win - a limit an elementary resolution argument shows is shared by every binned instrument, the calibration error included.

Non-asymptotic implicit bias of logistic regression at early-stage gradient descent dynamics

Gradient descent has been of particular interest in modern machine learning beyond sole focus on optimization. Implicit bias emerging from optimization, though not being encoded by the learning objective, often prevents from overfitting to spurious patterns. A typical instance is the max-margin implicit bias of a linear classifier, widely established for exponentially tailed loss functions. Even after having a given dataset separated, the parameter vector continues to evolve towards the max-margin direction asymptotically along the gradient descent dynamics. This phenomenon corroborates a frequent empirical observation of "train longer, generalize better." However, the max-margin convergence is an asymptotic phenomenon, and what is worse, this asymptotic convergence rate is significantly slower than pure convex optimization. Even so, the parameter vector along gradient descent dynamics commonly correlates with the max-margin direction positively (though not exactly) within considerably fewer iterations than the asymptotic rate. By shedding another light on this classical problem, this work aims to understand the mechanism of this early-stage alignment phenomenon. Our theoretical results demonstrate that the parameter vector weakly aligns with the max-margin direction within $O(\exp(\exp(-δ)))$ iterations, where $δ>0$ is the permissible alignment error, which is shown to be tight. By tracking the radial and tangential flows, our proof operates on the alignment dynamics directly with dataset geometry and gets rid of the asymptotic expansion, which is a key insight to establishing faster weak alignment.

Prediction-Only Distillation in Linear and Logistic Regression

Self-distillation (SD) is typically studied when the student is retrained on the teacher's original training inputs. In many practical deployments, however, the labeled training data are no longer available, and one has access only to the trained predictor and fresh unlabeled covariates. We study SD in this prediction-only regime through a fresh-X prediction-mixed scheme: a pure-distilled student is trained on fresh covariates pseudo-labeled by the teacher, and the final predictor is an affine combination of the teacher and student predictions. For ridge regression under proportional asymptotics, we derive deterministic equivalents for the optimally mixed prediction risk under general anisotropic covariance and deterministic signal. We show that this risk is strictly smaller than the teacher risk for almost every pair of teacher and student regularization levels, including when the fresh covariates are out-of-distribution and even when their covariance is isotropic. We further show that the optimal mixing weight cannot be identified from unlabeled data alone, but can be consistently estimated in a single post-training step using a small independent labeled calibration set, without additional model fitting. Finally, for binary logistic regression, we show that prediction mixing can outperform both the teacher and the pure-distilled classifier.

Who Became Financially Vulnerable After COVID-19? A Population-Level Machine Learning Analysis Using MEPS Data

The cost of healthcare remains a concern in the United States and may have been influenced by disruptions associated with the COVID-19 pandemic. This study examines healthcare financial vulnerability before and after the pandemic using Medical Expenditure Panel Survey (MEPS) data from 2019 and 2021. High financial burden was defined as out-of-pocket healthcare expenditures exceeding 10% of family income. Survey-weighted subgroup analyses were performed to obtain nationally representative estimates across demographic and socioeconomic groups. Descriptive analyses were complemented by interpretable logistic regression and machine learning models. Logistic regression was used to estimate adjusted odds ratios, while random forest and gradient boosting models were used to evaluate predictive performance. Temporal generalization assessed whether models trained on pre-pandemic data remained predictive when applied to post-pandemic observations. Financial vulnerability was strongly associated with poverty status, insurance coverage, and prescription drug spending. Subgroup analyses indicated persistent disparities across population groups, with some evidence of increased burden among vulnerable populations in 2021. Despite these differences, models trained on pre-pandemic data exhibited only modest reductions in predictive performance when evaluated on post-pandemic data, suggesting that the principal predictors of healthcare financial vulnerability remained relatively stable over time. These findings provide a population-level assessment of healthcare financial vulnerability during the COVID-19 period and demonstrate the value of combining interpretable statistical modeling with machine learning for population health research. The results may support future population health surveillance, risk stratification, and healthcare policy research aimed at reducing financial barriers to care.

Predicting Fruit Quality with a Hybrid Machine Learning and Image Processing Approach

Fruit spoilage is a significant issue in agriculture, leading to substantial economic losses. Addressing this, our study introduces a hybrid approach combining image processing and deep learning to assess fruit freshness. We developed an image processing algorithm that quantifies spoilage on a scale from 0 (fully fresh) to 100 (fully rotten). Alongside, we trained a convolutional neural network (CNN) to perform binary classification (fresh or rotten) using a large dataset of fruit images. The outcomes of both methods were synthesized using logistic regression to enhance the accuracy of freshness predictions. Subsequently, this logistic regression model was utilized to enable the image processing algorithm to provide binary classification based on its percentage output, thus eliminating the need for the CNN in real-time applications. Our approach, which does not require high computational resources, achieved real-time performance and was validated with over 90% accuracy on a dataset comprising apples and oranges. The primary limitation lies in the requirement for fruits to be isolated on a background that must be either white or transparent, suggesting future improvements could include advanced segmentation models to automate background removal. This study's results highlight the potential of integrating simple image processing techniques with machine learning to provide practical solutions in the agricultural sector.

Finite-Sample Performance of Gradient Descent in Logistic Regression with Gaussian Design

We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter $θ^*\in \mathbb{R}^d$ ($\|θ^*\|_2\ge 1$) from $n$ i.i.d. samples $\{(x_i,y_i)\}_{i=1}^n$, where $x_i\sim N(0,I_d)$ and $y_i|x_i \sim {\rm Bernoulli}(1/(1+\exp(-x_i^\top θ^*)))$. Our main aim is to characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD) on the maximum likelihood objective (i.e., the logistic loss). Under small $O(1)$ stepsize and $0$ initialization, we show that GD linearly converges to a small neighborhood of $θ^*$ achieving an $\ell_2$ error of order $O(\sqrt{\|θ^*\|_2^5d/n})$. This substantially goes beyond existing theoretical results that lack non-asymptotic estimation error rate and exhibit much slower parameter convergence. We also establish a faster local linear convergence to the same statistical error under a large $Θ(\|θ^*\|_2)$ stepsize. The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC). To that end, we uniformly control the deviation of the gradient from its population counterpart by covering and peeling arguments, and then show that the population GD is a contraction by a delicate analysis based on the eigenvalues of population Hessian matrices. Finally, we build upon the recent work Matsumoto and Mazumdar (2025) and devise a novel efficient estimator that attains a sharper rate in high dimensions. This indicates that the existing non-asymptotic guarantees exhibit sub-optimal dependence on $\|θ^*\|_2$, and that in many regimes $Θ(\sqrt{\|θ^*\|_2d/n})$ is the tight estimation error rate. Numerical examples are provided to corroborate our theoretical results.

Joint Nuclear and $\ell_1$ Regularization for Logistic Matrix Regression with Applications to Brain Imaging

We introduce a new convex optimization framework for logistic scalar-on-matrix regression which incorporates nuclear and $\ell_1$ norm penalties to enforce simultaneously low-rank and sparse structures in the estimated coefficient matrix. The proposed method enables interpretable modeling of high-dimensional matrix-valued predictors in the presence of binary responses. We derive a custom algorithm based on the Alternating Direction Method of Multipliers (ADMM) to efficiently solve the resulting convex optimization problem and establish the theoretical properties of the obtained solution. Numerical experiments clearly demonstrate the effectiveness of our method in recovering meaningful predictive patterns. Finally, we apply our method to the brain imaging data to identify structures in functional brain connectivity matrices that are characteristic of subjects with a family history of alcohol use disorders (AUDs).

A Comparative Analysis of Machine Learning and Deep Learning Models for Tweet Sentiment Classification: A Case Study on the Sentiment140 Dataset

The exponential growth of social media has created an urgent need for automated systems to analyze unstructured public sentiment in real time. This study compares a traditional Logistic Regression model using TF-IDF features with a deep learning Bidirectional Long Short-Term Memory (BiLSTM) architecture on a 10,000-tweet subset of the Sentiment140 dataset. Experimental results show that Logistic Regression outperformed BiLSTM, achieving an accuracy of 73.5% compared with 69.17%, while the deep learning model exhibited mild overfitting. These findings suggest that for medium-scale informal text data, classical machine learning with robust feature extraction can outperform more complex deep learning approaches. Finally, the trained models were integrated into an interactive web application using Streamlit and deployed on Hugging Face Spaces for public access.