Dense large language models(LLMs) face critical efficiency bottlenecks as they rigidly activate all parameters regardless of input complexity. While existing sparsity methods(static pruning or dynamic activation) address this partially, they either lack adaptivity to contextual or model structural demands or incur prohibitive computational overhead. Inspired by human brain's dual-process mechanisms - predictive coding (N400) for backbone sparsity and structural reanalysis (P600) for complex context - we propose CLADA, a \textit{\textbf{C}ognitive-\textbf{L}oad-\textbf{A}ware \textbf{D}ynamic \textbf{A}ctivation} framework that synergizes statistical sparsity with semantic adaptability. Our key insight is that LLM activations exhibit two complementary patterns: 1) \textit{Global statistical sparsity} driven by sequence-level prefix information, and 2) \textit{Local semantic adaptability} modulated by cognitive load metrics(e.g., surprisal and entropy). CLADA employs a hierarchical thresholding strategy: a baseline from offline error-controlled optimization ensures 40\%+ sparsity, dynamically adjusted by real-time cognitive signals. Evaluations across six mainstream LLMs and nine benchmarks demonstrate that CLADA achieves \textbf{~20\% average speedup with <2\% accuracy drop}, outperforming Griffin (5\%+ degradation) and TT (negligible speedup). Crucially, we establish the first formal connection between neurolinguistic event-related potential (ERP) components and LLM efficiency mechanisms through multi-level regression analysis ($R^2=0.17$ for sparsity-adaptation synergy). Requiring no retraining or architectural changes, CLADA offers a deployable solution for resource-aware LLM inference while advancing biologically-inspired AI design. Our code is available at \href{https://github.com/Oldify/CLADA}{CLADA}.

Understanding convergent learning -- the extent to which artificial and biological neural networks develop similar representations -- is crucial for neuroscience and AI, as it reveals shared learning principles and guides brain-like model design. While several studies have noted convergence in early and late layers of vision networks, key gaps remain. First, much existing work relies on a limited set of metrics, overlooking transformation invariances required for proper alignment. We compare three metrics that ignore specific irrelevant transformations: linear regression (ignoring affine transformations), Procrustes (ignoring rotations and reflections), and permutation/soft-matching (ignoring unit order). Notably, orthogonal transformations align representations nearly as effectively as more flexible linear ones, and although permutation scores are lower, they significantly exceed chance, indicating a robust representational basis. A second critical gap lies in understanding when alignment emerges during training. Contrary to expectations that convergence builds gradually with task-specific learning, our findings reveal that nearly all convergence occurs within the first epoch -- long before networks achieve optimal performance. This suggests that shared input statistics, architectural biases, or early training dynamics drive convergence rather than the final task solution. Finally, prior studies have not systematically examined how changes in input statistics affect alignment. Our work shows that out-of-distribution (OOD) inputs consistently amplify differences in later layers, while early layers remain aligned for both in-distribution and OOD inputs, suggesting that this alignment is driven by generalizable features stable across distribution shifts. These findings fill critical gaps in our understanding of representational convergence, with implications for neuroscience and AI.

Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data science. Over the past decade, screening rules have risen in popularity as a way to eliminate features when producing the sparse regression weights of $L_1$ models. However, despite the increasing need of privacy-preserving models for data analysis, to the best of our knowledge, no differentially private screening rule exists. In this paper, we develop the first private screening rule for linear regression. We initially find that this screening rule is too strong: it screens too many coefficients as a result of the private screening step. However, a weakened implementation of private screening reduces overscreening and improves performance.

Groundwater is eventually undermined by human exercises, such as fast industrialization, urbanization, over-extraction, and contamination from agrarian and urban sources. From among the different contaminants, the presence of heavy metals like cadmium (Cd), chromium (Cr), arsenic (As), and lead (Pb) proves to have serious dangers when present in huge concentrations in groundwater. Long-term usage of these poisonous components may lead to neurological disorders, kidney failure and different sorts of cancer. To address these issues, this study developed a machine learning-based predictive model to evaluate the Groundwater Quality Index (GWQI) and identify the main contaminants which are affecting the water quality. It has been achieved with the help of a hybrid machine learning model i.e. LCBoost Fusion . The model has undergone several processes like data preprocessing, hyperparameter tuning using Differential Evolution (DE) optimization, and evaluation through cross-validation. The LCBoost Fusion model outperforms individual models (CatBoost and LightGBM), by achieving low RMSE (0.6829), MSE (0.5102), MAE (0.3147) and a high R$^2$ score of 0.9809. Feature importance analysis highlights Potassium (K), Fluoride (F) and Total Hardness (TH) as the most influential indicators of groundwater contamination. This research successfully demonstrates the application of machine learning in assessing groundwater quality risks in Odisha. The proposed LCBoost Fusion model offers a reliable and efficient approach for real-time groundwater monitoring and risk mitigation. These findings will help the environmental organizations and the policy makers to map out targeted places for sustainable groundwater management. Future work will focus on using remote sensing data and developing an interactive decision-making system for groundwater quality assessment.

In statistics, generalized linear models (GLMs) are widely used for modeling data and can expressively capture potential nonlinear dependence of the model's outcomes on its covariates. Within the broad family of GLMs, those with binary outcomes, which include logistic and probit regressions, are motivated by common tasks such as binary classification with (possibly) non-separable data. In addition, in modern machine learning and statistics, data is often high-dimensional yet has a low intrinsic dimension, making sparsity constraints in models another reasonable consideration. In this work, we propose to use and analyze an iterative hard thresholding (projected gradient descent on the ReLU loss) algorithm, called binary iterative hard thresholding (BIHT), for parameter estimation in sparse GLMs with binary outcomes. We establish that BIHT is statistically efficient and converges to the correct solution for parameter estimation in a general class of sparse binary GLMs. Unlike many other methods for learning GLMs, including maximum likelihood estimation, generalized approximate message passing, and GLM-tron (Kakade et al. 2011; Bahmani et al. 2016), BIHT does not require knowledge of the GLM's link function, offering flexibility and generality in allowing the algorithm to learn arbitrary binary GLMs. As two applications, logistic and probit regression are additionally studied. In this regard, it is shown that in logistic regression, the algorithm is in fact statistically optimal in the sense that the order-wise sample complexity matches (up to logarithmic factors) the lower bound obtained previously. To the best of our knowledge, this is the first work achieving statistical optimality for logistic regression in all noise regimes with a computationally efficient algorithm. Moreover, for probit regression, our sample complexity is on the same order as that obtained for logistic regression.

The aim of this thesis is to extend the applications of the Quantile Regression Forest (QRF) algorithm to handle mixed-frequency and longitudinal data. To this end, standard statistical approaches have been exploited to build two novel algorithms: the Mixed- Frequency Quantile Regression Forest (MIDAS-QRF) and the Finite Mixture Quantile Regression Forest (FM-QRF). The MIDAS-QRF combines the flexibility of QRF with the Mixed Data Sampling (MIDAS) approach, enabling non-parametric quantile estimation with variables observed at different frequencies. FM-QRF, on the other hand, extends random effects machine learning algorithms to a QR framework, allowing for conditional quantile estimation in a longitudinal data setting. The contributions of this dissertation lie both methodologically and empirically. Methodologically, the MIDAS-QRF and the FM-QRF represent two novel approaches for handling mixed-frequency and longitudinal data in QR machine learning framework. Empirically, the application of the proposed models in financial risk management and climate-change impact evaluation demonstrates their validity as accurate and flexible models to be applied in complex empirical settings.

Interpreting data is central to modern research. Large language models (LLMs) show promise in providing such natural language interpretations of data, yet simple feature extraction methods such as prompting often fail to produce accurate and versatile descriptions for diverse datasets and lack control over granularity and scale. To address these limitations, we propose a domain-agnostic method for dataset featurization that provides precise control over the number of features extracted while maintaining compact and descriptive representations comparable to human expert labeling. Our method optimizes the selection of informative binary features by evaluating the ability of an LLM to reconstruct the original data using those features. We demonstrate its effectiveness in dataset modeling tasks and through two case studies: (1) Constructing a feature representation of jailbreak tactics that compactly captures both the effectiveness and diversity of a larger set of human-crafted attacks; and (2) automating the discovery of features that align with human preferences, achieving accuracy and robustness comparable to expert-crafted features. Moreover, we show that the pipeline scales effectively, improving as additional features are sampled, making it suitable for large and diverse datasets.

The paper presents an innovative methodology for designing frequency selective surface (FSS) based radar absorbing materials using machine learning (ML) technique. In conventional electromagnetic design, unit cell dimensions of FSS are used as input and absorption coefficient is then predicted for a given design. In this paper, absorption coefficient is considered as input to ML model and image of FSS unit cell is predicted. Later, this image is used for generating the FSS unit cell parameters. Eleven different ML models are studied over a wide frequency band of 1GHz to 30GHz. Out of which six ML models (i.e. (a) Random Forest classification, (b) K- Neighbors Classification, (c) Grid search regression, (d) Random Forest regression, (e) Decision tree classification, and (f) Decision tree regression) show training accuracy more than 90%. The absorption coefficients with varying frequencies of these predicted images are subsequently evaluated using commercial electromagnetic solver. The performance of these ML models is encouraging, and it can be used for accelerating design and optimization of high performance FSS based radar absorbing material for advanced electromagnetic applications in future.

Motivated by the great success of Bayesian additive regression trees (BART) on regression, we propose a nonparametric Bayesian approach for the function-on-scalar regression problem, termed as Functional BART (FBART). Utilizing spline-based function representation and tree-based domain partition model, FBART offers great flexibility in characterizing the complex and heterogeneous relationship between the response curve and scalar covariates. We devise a tailored Bayesian backfitting algorithm for estimating the parameters in the FBART model. Furthermore, we introduce an FBART model with shape constraints on the response curve, enhancing estimation and prediction performance when prior shape information of response curves is available. By incorporating a shape-constrained prior, we ensure that the posterior samples of the response curve satisfy the required shape constraints (e.g., monotonicity and/or convexity). Our proposed FBART model and its shape-constrained version are the new advances of BART models for functional data. Under certain regularity conditions, we derive the posterior convergence results for both FBART and its shape-constrained version. Finally, the superiority of the proposed methods over other competitive counterparts is validated through simulation experiments under various settings and analyses of two real datasets.

Intelligent tutors have proven to be effective in K-12 education, though their impact on adult learners -- especially as a supplementary resource -- remains underexplored. Understanding how adults voluntarily engage with educational technologies can inform the design of tools that support skill re-learning and enhancement. More critically, it helps determine whether tutoring systems, which are typically built for K-12 learners, can also support adult populations. This study examines the adoption, usage patterns, and effectiveness of a novel tutoring system, Apprentice Tutors, among adult learners at a state technical college. We analyze three types of data including, user demographics, grades, and tutor interactions, to assess whether voluntary tutor usage translates into measurable learning gains. Our findings reveal key temporal patterns in tutor engagement and provide evidence of learning within tutors, as determined through skill improvement in knowledge components across tutors. We also found evidence that this learning transferred outside the tutor, as observed through higher course assessment scores following tutor usage. These results suggest that intelligent tutors are a viable tool for adult learners, warranting further research into their long-term impact on this population.