Computer Science and Mathematics

Abstract: Sparse longitudinal transaction data create a statistical-learning problem in which low basket occupancy, combinatorial candidate growth, temporal heterogeneity, and data-quality sensitivity complicate interpretable pattern discovery. This study proposes a reproducible, sparsity-aware framework that separates global distributional characterization, unsupervised co-occurrence learning, statistical qualification, adjusted outcome modeling, and transparent prioritization. The empirical application comprises 31,157 baskets, 139,396 valid item lines, 710 products, and 762 active days; the 31,157 × 710 basket-product representation has 0.630% density. Multiplicity-screened association-rule learning retains 1,174 directional rules. In a strictly subsequent validation period, 93.6% of discovery rules preserve lift above one, 49.3% satisfy all prespecified thresholds again, and rank correlations for support, confidence, and lift range from 0.803 to 0.849. An estimated-dispersion NB2 model with day-clustered uncertainty preserves the principal basket-breadth associations, while Gamma sensitivity analysis confirms the direction, but not invariant magnitude, of late-service basket-value effects. The results show that sparse transactional structure is studied more defensibly when algorithmic discovery is explicitly separated from multiplicity screening, statistical inference, temporal replication, and decision prioritization. Because the empirical evaluation is a longitudinal single case, the reported effect magnitudes remain case-specific; the transferable contribution is the auditable statistical-learning procedure.

Abstract: Continuous dequantization embeds discrete data into a continuous space, but the relaxation may alter the statistical information in the original categories. We study weighted discrete laws for which dequantization must be lossless under a prescribed quantizer. Any partition-respecting, parameter-independent kernel generates a continuous experiment Blackwell equivalent to the discrete one, preserving likelihood-based inference, Fisher information, Bayes posteriors, and optimal risks before downstream approximation. For finite-capacity continuous models, we derive an exact KL decomposition into re-quantized categorical error and within-cell shape error. This motivates a model-aware family of exact truncated-Gibbs dequantizers that trades entropy against geometric displacement while preserving exact category recovery. We derive transport, reconstruction, leakage, geometry-perturbation, and finite-sample selection guarantees. Experiments with Gaussian mixtures and rational-quadratic spline flows verify the identities and show that tuning the Gibbs concentration can materially reduce re-quantized error. Two real-data applications to Abalone ring counts and RAND physician-visit counts further demonstrate that exact dequantization improves reconstruction of the underlying discrete distribution relative to fitting the same smooth continuous model directly to the atoms.

Abstract: Typical machine learning forecasting approaches, optimized via mean squared error, struggle in decision settings requiring directional consistency. The Maximum Agreement Linear Predictor (MALP) framework addresses this by maximizing Lin’s Concordance Correlation Coefficient (CCC), but its meta-learner value under real, weak-signal conditions is untested. We evaluate a two-stage MALP-Meta architecture (four base models, a CCC-optimized meta-learner) on real hourly S&P 500 (SPY) data (n = 5032; 2023–2026), with every result cross-validated across two computing environments. Only Ridge achieves significant directional accuracy (52.7%, p = 0.037); no MALP-Meta variant improves on this, and we diagnose a previously undocumented pathology in which CCC optimization collapses toward a constant under weak signal. Of three temporal robustness strategies, only stable feature selection matches Ridge’s significance (52.5%, p = 0.048). Under an externally-defined stress regime (VIX>25), one meta-learner configuration improves simultaneously on concordance and direction, an unconfirmed signal (p = 0.291). Sensitivity analysis shows the primary result is fragile to the evaluation split. These findings affirm rather than overturn the conventional agreement–error trade-off: agreement-based meta-learning’s real-world value is modest, conditional on genuine market stress, and detectable only through rigorous cross-validation and sensitivity analysis.

Abstract: Smartphone-based human activity recognition (HAR) uses features collected from smartphone sensors to distinguish between different human activities. The large number of correlated features generated by smartphone sensors can make feature selection and model interpretation challenging. This study evaluates a two-stage feature selection and classification framework for HAR, in which sparse partial least squares discriminant analysis (sPLS-DA) is used primarily as a supervised feature selection method, while multinomial logistic regression is employed as the subsequent classifier. The approach is compared with LASSO and Elastic Net regularization under consistent training, testing, and cross-validation procedures. The experiment used 30 repetitions. In each repetition, 21 subjects were used for training and nine subjects were used for testing, with five-fold subject-level cross-validation inside the training set. The original variables selected by each method were also tested with the same unpenalized multinomial logistic regression (MLR) classifier. Native LASSO and Elastic Net gave the highest predictive performance, with mean accuracies of 0.9514 ± 0.0166 and 0.9504 ± 0.0187, respectively, and mean multiclass AUC values of about 0.997. LASSO selected 169.8 ± 25.4 features on average, while Elastic Net selected 255.5 ± 114.4. sPLS-DA selected 353.7 ± 47.5 features on average, while its native max.dist classifier reached a mean accuracy of 0.8831 ± 0.0283 and the selected feature sets had the highest mean pairwise Jaccard overlap (0.6611). Using unpenalized MLR on the selected feature subsets reduced accuracy for all three methods. Overall, LASSO gave the best balance between predictive performance and a smaller feature set, while sPLS-DA showed higher feature-set overlap but kept many more features. These results show that predictive performance, feature-set size, and selection stability should be considered together in smartphone-based HAR.

Abstract: A hierarchical Ornstein–Uhlenbeck stochastic differential equation with event-conditional drift is fitted to monthly text-derived affect trajectories from a self-disclosure-rich Reddit subreddit (2023–2024; 254,153 users, 324,548 user-months), with the death of a close family member as the adverse life event. Event dates are recovered from free text by three regex classes of increasing specificity — coarse, explicit and recent — forming a within-corpus precision ladder. The ladder gives the first real-data test of the posterior-bias bound of a companion paper by the present authors, which predicts that the recovered drift magnitude grows as event-date precision tightens. The prediction is confirmed on the coarse-to-explicit step (mean drift −0.109 to −0.157 standardised VADER units; adjusted p from 0.041 to 0.008), whereas the explicit-to-recent step is underpowered because the recency filter cuts the subject pool threefold. We document this precision–power tradeoff and propose the regex ladder as a reusable proxy for event-date precision.

Abstract: We develop a hierarchical Ornstein–Uhlenbeck stochastic differential equation with event-conditional drift for latent-state dynamics around life events detected in text. Three formal results are established: existence and uniqueness of strong solutions; identifiability of the population-level parameters under sparse panel observation; and a posterior-bias bound for the drift estimator when event dates are known only to a coarser precision Δ than the observation grid. Inference combines a bootstrap particle filter with a Liu–West shrinkage kernel for the static hyperparameters, validated on synthetic data and against the exact Kalman posterior in the Gaussian special case. An empirical demonstration on approximately 1.7×10⁵ Reddit posts (2023-01 to 2024-12) estimates pre-event drift for four event types (n=696 users): none survives Benjamini–Hochberg correction, giving a calibrated null for the adequately powered job-change type and an underpowered non-detection for the other three.

Abstract: A multitude of phenomena of interest are indexed in space, where the distribution of the response variable is a mixture of discrete and continuous random variables. We propose a spatial model in which the response variable follows a mixed discrete continuous distribution, with a probability mass at zero and a continuous gamma component for positive values. This distribution is known as the zero adjusted gamma distribution. The model is based in two submodels. The probability mass at zero is formulated using logistic regression. For the continuous positive data, a quasi-likelihood model under the gamma distribution is adopted. Spatial dependence is incorporated into both submodels. Inferential aspects are discussed, and the performance of the estimators is assessed through a simulation study. Expressions for standard errors are derived and residuals are proposed to evaluate the goodness of fit. The local influence methodology is used to identify potentially influential observations. The proposed approach is illustrated through the analysis of both simulated and real data. In the real data, the amount of precipitation accumulated (in mm) during August 2021 in the state of Pernambuco, Brazil, is analyzed.

Abstract: In this paper, recurrent MAP flows are constructed using a Markov?modulated Poisson process. Given the deterministic dead time for these flows, recurrent observation flows are determined. Dead times are estimated as the minimum distances between adjacent observation times. The validity of these estimates is proved using an upper bound for the jump size of the random walk defined by the recurrent MAP flow. This upper bound is investigated using the continuity theorem for uniformly convergent series of continuous functions and the Weierstrass theorem on the maximum of a continuous function on a segment.

Abstract: This study provides a unified theoretical and empirical examination of the generalized hyperbolic (GH) distribution family. The special and limiting relationships among the GH distribution and its important subclasses are reviewed. The empirical analysis considers daily returns on the SPDR SP 500 ETF Trust (SPY) from January 4, 2010, to July 22, 2024. The unrestricted GH distribution and its variance–gamma(VG), normal–inverse Gaussian (NIG), normal reciprocal inverse Gaussian (NRIG), hyperbolic (H), and HA subclasses are estimated by maximum likelihood method. Overall, the results demonstrate that the GH family provides a flexible and effective alternative to the Gaussian benchmark, although the preferred subclass depends on whether predictive adequacy or model parsimony is emphasized.

Abstract: “Correlation does not imply causation,” the adage warns. But how does correlation relate to causation? For linear stochastic dynamical systems driven by white noise, a widely used class of models across the natural and social sciences, the question has an exact answer. At steady state, correlation (more precisely covariance) and causation are linked by the Lyapunov equation. From this equation we derive closed-form expressions for pairwise correlation coefficients as explicit functions of the causal parameters and noise variances. We analyze these expressions for nine network topologies and unpack seven insights regarding the relationship between correlation and causation. For instance, we illustrate through some examples that causation is transitive, while correlation is not; and that the mapping from causation to correlation is generally many-to-one. The formulae also reveal that the covariance between any two variables is a linear combination of the noise variances, with weights that are highly nonlinear functions of the causal parameters. This is one of the reasons that the relationship between correlation and causation resists simple intuition. We show that the formulae from the fully connected three-node network serve as the “master formulae” for 3 ×3 networks, because of the structural symmetry of its topology, and can be reduced to the formulae for every sparser three-node network as causal connections are set to zero. Finally, we note that the Lyapunov equation is a unifying mathematical object for causal modeling frameworks such as Granger causality and dynamic causal modeling, with additive white noise assumption.

Abstract: Existing randomness conditioning methods face a fundamental dilemma: heuristic post-processing lacks rigorous mathematical uniformity guarantees, while provable seeded extractors require an independent perfectly uniform seed, merely shifting the trust assumption. We present a universal, mathematically certified conditioning framework that resolves this dilemma. For any NIST SP~800-90B ESV-certified entropy source, regardless of bias or implementation, our framework generates a provably uniform output stream without requiring any external seed or heuristic whitening. The core contribution is the Geometric Convergence Theorem (GCT), proving that the modular reduction of a negative binomial counting variable \( N_p \sim \mathrm{NB}(m, p) \)—where m denotes the required number of successes generated from fixed ESV entropy blocks via Bernoulli trials with success probability p—converges exponentially to uniformity over \( \mathbb{Z}_R \), with spectral radius \( \rho_{\mathrm{NB}} = p / \sqrt{p^2 + 4(1-p)\sin^2(\pi/R)} < 1 \). A Practical Entropy Budgeting mechanism ensures information-theoretic entropy conservation via a fixed input-output ratio. In a large-scale validation generating 100 MB of output from a biased ESV source (\( H_{\mathrm{in}} \) =3.32 bits/byte), the framework achieved Shannon entropy 7.999998 bits/byte and Min-Entropy 7.9936 bits/byte, approaching the theoretical lower bound of 7.9949 bits/byte to within 0.0013 bits/byte, with\( \chi^2 = 275.95 \) (df = 255). This establishes the first seedless, provable, and platform-agnostic conditioning framework for certified entropy sources.

Abstract: Many scientific problems are fundamentally relational: the quantity of interest is a connection between two objects, while the information that describes similarity is available for the objects themselves. This mismatch is common in brain networks, molecular interactions, and other high-dimensional systems. We develop a covariance framework for unordered relationships that transfers object-level geometry to the relations they form while preserving endpoint identity and invariance to ordering. Building on symmetric pairwise-kernel representations, we develop new theory for the loop-free domains used in undirected networks. We establish spectral interlacing and trace-loss results after self-pairs are removed, connect the relational spectrum to regularization and risk, derive an exact inferential error for spectral truncation, and quantify how perturbations of the underlying geometry propagate to the pair covariance and estimator. Simulations show when structured borrowing improves estimation and when geometric misspecification can erode that benefit. We then apply the framework to autism neuroimaging using resting-state functional-connectivity data from the Autism Brain Imaging Data Exchange (ABIDE). The analysis considers a 116-region brain parcellation, yielding 6,670 unique functional connections, and shows that this large connectome can have a far smaller effective covariance dimension. The application also demonstrates that high explained covariance alone is not sufficient for choosing a low-rank representation when the goal is to preserve inferential accuracy. These results illustrate how biologically meaningful information defined at the brain-region level can organize dependence among connections while retaining the connection itself as the inferential unit. The framework provides a principled foundation for covariance and regularization when the statistical units are unordered relationships.

Abstract: Extreme wind speed poses significant risks to the economy in areas such as infrastructure and agriculture in South Africa, particularly in semiarid regions such as the Northern Cape. In minimizing such risks, accurate modelling of extreme wind speed is essential for disaster preparedness and climate adaptation. In this pursuit, Hybrid Generalised Additive Extreme Value (GAEV) models have been used in climate studies, where the extreme value parameters are allowed to evolve smoothly through spline functions of the covariates to improve forecasts. However, such applications remain limited and scattered across literature. Furthermore, comparative evaluations of the performance of the hybrid models estimated via frequentist and Bayesian estimation approaches with applications to extreme wind speed remain scarce, particularly within semi-arid regions of South Africa. This creates a gap in both literature which the study seeks to bridge. To achieve this, we estimate the hybrid GAEV models via frequentist (maximum likelihood) and Bayesian methods using extreme wind speed data from Kimberley and Upington in the Northern Cape Province of South Africa. We then compare the performance of the two estimation frameworks using metrics such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The results shows that the Bayesian GAEV consistently outperformed the frequentist approach, producing lower error values in both in-sample and out-of-sample forecasts. This demonstrates the Bayesian framework’s superior ability to capture non-linear covariate effects and tail behaviour in extreme wind distributions. The findings highlight the importance of Bayesian GAEV models for reliable forecasting of extreme wind speeds in vulnerable regions. Policymakers and disaster management agencies should adopt Bayesian based approaches to improve risk assessment and preparedness strategies. Future research should extend the analysis to additional provinces, incorporate longer datasets, and explore broader climatic drivers to enhance generalisability and strengthen climate resilience planning.

Abstract: In the application of Bayesian methods, the choice of a prior density for defined model parameters is often a practical issue. In scientific and medical applications, it requires careful justification. In many settings, the properties of the statistical likelihood function and the overall statistical model, within which the model parameters are defined, are useful in justifying the chosen prior density. In some settings this is extended to matching Bayesian and frequentist model results. In this paper, prior density selections reflecting specific model related and matching properties are reviewed. It is further shown that if these considerations are extended to include the matching of likelihood and posterior density higher order derivatives, they provide new exclusionary rules for the selection of prior densities. In addition, the class of related acceptable prior densities are non-informative on a scale related to the Pratt-Arrow utility-based measure of relative risk. Multivariate extensions are briefly considered.

Abstract: Mathematical sociology has developed through partially independent programs concerned with exchange, status, mobility, organizations, social influence, collective action, and institutional trust. These traditions often share matrices, hazard rates, games, and differential equations while representing non-equivalent social objects. This survey reconstructs four foundational programs by substantive mechanism. Each model is written as a tuple comprising units, a state space with its social semantics, a structure, a transition law, an observation operator, parameters, and a source of identifying variation. The central result is a mechanism indistinguishability theorem: two transition laws are locally indistinguishable to first order at a common latent state exactly when their difference lies in the kernel of the differential of the observation operator, while equality of whole observed paths requires projectability. No increase in sample size under one observation design removes such non-identification. A corollary on aggregation explains why the mean of a population of logistic actors is not logistic, and a worked example shows that founding counts cannot separate organizational legitimation from competition. A worked cross-scale case study carries one chain from discrete adoption through continuum propagation to a first-passage reduction, with the status of every claim stated explicitly.

Abstract: Multiple nonparametric regression provides a flexible framework for modeling complex relationships between a response variable and multiple covariates without imposing restrictive parametric assumptions. In practical applications, covariates and/or responses are often partially observed, leading to substantial methodological challenges. This paper develops a unified conceptual and theoretical analysis of the role played by the variance–covariance structure of covariates and the response in multiple nonparametric regression under missing data. We show that, although the variance–covariance matrix does not parameterize the regression function itself, it governs identifiability, stability, efficiency, and inferential validity through its influence on local smoothing geometry. Particular emphasis is placed on how different missingness mechanisms distort covariance structures and thereby affect kernel-based and local polynomial estimators. The paper provides a foundational perspective for principled estimation and inference in incomplete-data nonparametric regression models.

Abstract: Many practical questions are causal: they ask what would happen to an outcome if we changed a treatment, a price, or a policy. Answering such questions from data requires choosing an estimation method and, before that, deciding whether the question can be answered at all from the available data and assumptions. Both decisions are error prone, and wrong choices can produce answers that look precise while being wrong. We introduce the Causal World Foundation Model (CWFM), a hybrid system in which a neural network, pretrained on a large collection of synthetic causal problems, orchestrates a library of classical causal estimators that are fitted anew to each submitted dataset. Before any estimation, deterministic gates check a declared contract of identification and support conditions. Queries that fail these checks receive a structured refusal with a machine-readable reason instead of a number, and the uncertainty of every answer is calibrated with split conformal prediction. On a locked synthetic benchmark spanning static, randomized, and network-interference settings, CWFM matches the accuracy of the best fixed baseline without knowing which mechanism generated each dataset, keeps its intervals close to the nominal coverage, and refuses every query whose declared conditions fail while the baselines answer all of them. A confirmatory round under a frozen protocol, including a semi-synthetic benchmark built on real energy-sensor covariates, reproduces these findings and sharpens them: all point estimates come from the classical estimator blend, and simple non-neural aggregation baselines match or slightly exceed the pretrained router's accuracy. The demonstrated value of the system therefore lies in the contract, gating, and calibration layer around classical estimation, a practical and transferable role for pretrained causal systems.

Abstract: Commodity futures markets constitute a complex system. The price time series, as manifestations of their intrinsic dynamics, exhibit pronounced non-stationarity, nonlinearity, and multifractal characteristics. Traditional linear models and single-scale analytical frameworks are fundamentally inadequate for capturing the intrinsic dynamical features of such complex systems. Therefore, this paper employs a comprehensive multiscale non-stationary time series analytical framework, integrating four methodologies—multifractal cross-correlation analysis, multiscale complexity measures, time irreversibility diagnostics, and structural break detection—to investigate the non-stationary and nonlinear dynamical features of commodity futures markets. Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) is used to quantify the scale-dependent cross-correlations among WTI crude oil, the US dollar index, and cross-market soybean prices. The Porat–Friedland (PG) irreversibility index measures time-asymmetry across multiple investment horizons. Multiscale Weighted Permutation Entropy (MSWPE) characterizes the complexity hierarchy along the soybean crushing chain (soybean → meal → oil). Jensen–Shannon (JS) divergence-based segmentation detects structural breaks in the WTI price series. We uncover three intriguing phenomena that reveal the characteristics of commodity futures markets as a complex system. First, the scale dependence of market dynamics is not homogeneous across commodities but is fundamentally shaped by supply adjustment elasticity. Energy commodities exhibit pronounced scale-dependent amplification and directional sign reversal at intermediate horizons, while globally tradable agricultural commodities maintain near-monofractal structures across scales, absorbing external shocks as localized noise. Second, through consistent results obtained across multiple analytical methods, we identify an inherent frequency in the market—a characteristic time scale of approximately 20 days—which emerges as the coupling anchor between physical logistics rhythms and financial pricing, potentially representing the intrinsic frequency at which markets digest shocks and complete directional transitions. Third, the persistence of structural reconstruction following shocks depends on the systemic penetration depth of shocks, with exogenous macroeconomic uncertainty exerting stronger and more lasting effects than market-internal events. In summary, supply elasticity, physical logistics rhythms, and systemic penetration depth together constitute the three fundamental determinants of nonlinear dynamics in commodity futures markets, with significant implications for cross-commodity allocation, multi-horizon risk management, and geopolitical scenario analysis.

Abstract: This article presents an innovative methodology that integrates Dual STATIS analysis with neutrosophic logic to evaluate the stability of the structure of relationships among financial variables in savings and credit cooperatives. The developed approach makes it possible to incorporate the uncertainty present in financial indicators and analyze their temporal evolution. Unlike classical STATIS, which focuses on similarity among cooperatives, the dual approach analyzes the covariance structure among the variables, identifying stable latent dimensions and turning points in the cooperative system. The results reveal patterns of structural stability and significant changes associated with relevant economic events, including the impact of the COVID-19 pandemic. The proposed methodology constitutes a useful alternative for strengthening financial supervision processes and supporting strategic decision-making in the cooperative sector.

Abstract: Modern non-stationary signal denoisers increasingly replace a global wavelet threshold by a \emph{detect-then-act} (gated) rule that first localises an artefact in the time--scale plane and then suppresses it selectively. Such gates couple sub-bands, and it has been unclear how to quantify, in a basis-intrinsic and interpretable way, \emph{how much} of the denoising performance is produced by that coupling. We introduce the \emph{interaction budget} \(I=1-\sum_j S_j\) and prove that it equals the normalised \(L^2\)-distance of the performance functional to the space of band-additive functions; hence \(I=0\) for any band-diagonal operator and \(I>0\) exactly when the gate couples bands. We then (i) give an exact pairwise identity for a binary gate, a two-point lower bound, and a sharp iff-condition on the gate; (ii) identify a coupling-strength functional with the leading-order law \(I(\kappa)=(\mathcal C/V_0)\kappa^2+o(\kappa^2)\); and (iii) bound the second-order HDMR/EMPR truncation error, which vanishes for single-trigger gates. Finally, for coloured noise---where the sub-band factors are correlated and \(I\) alone conflates the two effects---an EMPR product-support decomposition \emph{separates} operator-induced from correlation-induced interaction, with a correlation-invariant operator signature and a permutation-based estimator. Controlled experiments confirm all results.