arXiv subjects

Kōsaku Takanashi

Publications and source records attributed to Kōsaku Takanashi.

7 recordsLinked to original sources

arXiv2026

Fast boundary-aware spatial intensity estimation on complex domains

Spatial intensity maps are routinely used to summarize point patterns on geographically constrained regions, such as islands, coastlines, watersheds, ecological reserves, and administrative areas with physical barriers. In these settings, the domain is not a nuisance feature-- it determines where probability mass may be assigned and which locations should be smoothed together. Standard kernel density estimators can place mass outside the study region and smooth according to Euclidean distance, while diffusion-based estimators respect the geometry but are costly to recompute when the data subset, bandwidth, or evaluation grid changes. Motivated by repeated hotspot mapping of theft and larceny incidents on Oahu, Hawaii, we propose the projected diffusion kernel density estimator (PDKDE). PDKDE expands the Neumann diffusion kernel in a truncated Laplacian eigenbasis, so that the geometry of a fixed domain is computed once and subsequent density estimates are obtained through explicit spectral coefficients. The resulting estimator preserves the boundary-aware and geometry-respecting behavior of diffusion smoothing while making repeated estimation and least-squares cross-validation computationally practical. For the exact projected estimator, we prove MISE consistency and pointwise consistency up to the boundary. Controlled simulations show that PDKDE reduces boundary and barrier artifacts relative to Euclidean kernels and is substantially faster than the geometry-aware comparators considered after the one-time domain computation. In the Oahu application, the method produces coastline-constrained descriptive maps across time windows in seconds, illustrating its intended fixed-domain, changing-data use case.

stat.ME↗

arXiv2026

An Entropy-Energy Identity for Predictive Kullback-Leibler Regret in Infinitely Divisible Location Models

We consider predictive density estimation under logarithmic score for $d$-dimensional infinitely divisible location models. Taking the formal Bayes predictive density under the Lebesgue prior as a benchmark, we study the Kullback-Leibler regret of competing Bayes predictive densities. Our main contribution is an exact entropy-energy identity: the integrated regret of a Bayes predictive density $\hat{p}^π$ under prior $π$ relative to the benchmark admits an exact representation as the Dirichlet-form energy of the square-rooted marginal distribution $\sqrt{M^π}$ for the symmetric Markov semigroup induced by the benchmark kernel. This converts regret comparisons into a potential-theoretic problem and yields a sharp recurrence/transience characterization of when the benchmark predictive density can or cannot be uniformly improved. We introduce an $\mathcal{A}$-harmonic class of improper priors -- defined through the generator $\mathcal{A}$ of the induced process -- and give explicit tail conditions -- an integral test on the induced marginal, equivalent to power-law prior decay in heavy-tailed models -- that guarantee admissibility of the resulting Bayes predictive density. We illustrate the theory with new results for several distributions.

math.ST↗

arXiv2026

When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updating

Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that separates \emph{belief posteriors} -- conditional beliefs justified by the foundations of Savage and Anscombe-Aumann under a joint probability mode l-- from \emph{decision posteriors} -- randomized decision rules justified by preferences over decision rules. We make explicit that a loss-based posterior coincides with ordinary Bayes if and only if the loss is, up to scale and a data-only term, negative log-likelihood. We then show that generalized marginal likelihood is not evidence for decision posteriors, and Bayes factors are not well-defined without additional structure. In the decision posterior regime, non-degenerate posteriors require nonlinear preferences over decision rules. Under sequential coherence and separability, these lead to an entropy-penalized variational representation yielding generalized Bayes as the optimal rule.

stat.ME↗

arXiv2026

Optimal Hold-Out Size in Cross-Validation

Cross-validation (CV) is routinely used across the sciences to select models and tune parameters, and the resulting choices are often interpreted as substantive scientific conclusions (e.g., which variables, mechanisms, or risk factors are ``supported by the data''). A key part of the CV procedure -- the hold-out size, or equivalently the fold count $K$ -- is typically set by convention (e.g., 80/20, $K=5$) rather than by a principled criterion. Central to the issue is the tradeoff between training and testing: increasing the training sample size improves model accuracy, while sacrificing certainty around the accuracy itself. We formalize the tradeoff by targeting predictive performance and explicitly penalizing evaluation uncertainty, which cannot be identified from the data without additional assumptions. We derive finite-sample expressions of this evaluation uncertainty under symmetric errors and general upper bounds under broader error conditions, yielding a transparent utility-based rule for selecting the hold-out size as a function of an irreducible-noise parameter. Empirical analyses with linear regression and random forests across multiple domains, and a high-dimensional genomics application, show that (i) the choice of $K$ is dependent on the data and model. (ii) the optimal $K$ varies based on the assumption on the irreducible error, and (iii) the implied inferential conclusions can change materially as the irreducible error, and thus $K$, varies. The resulting framework replaces a one-size-fits-all convention with a context-specific, assumption-explicit choice of $K$, enabling more reliable model comparisons and downstream scientific inference.

stat.ME↗

arXiv2026

Dynamic causal inference with time series data

We generalize the potential outcome framework to time series with an intervention by defining causal effects on stochastic processes. Interventions in dynamic systems alter not only outcome levels but also evolutionary dynamics -- changing persistence and transition laws. Our framework treats potential outcomes as entire trajectories, enabling causal estimands, identification conditions, and estimators to be formulated directly on path space. The resulting Dynamic Average Treatment Effect (DATE) characterizes how causal effects evolve through time and reduces to the classical average treatment effect under one period of time. For observational data, we derive a dynamic inverse-probability weighting estimator that is unbiased under dynamic ignorability and positivity. When treated units are scarce, we show that conditional mean trajectories underlying the DATE admit a linear state-space representation, yielding a dynamic linear model implementation. Simulations demonstrate that modeling time as intrinsic to the causal mechanism exposes dynamic effects that static methods systematically misestimate. An empirical study of COVID-19 lockdowns illustrates the framework's practical value for estimating and decomposing treatment effects.

stat.ME↗

arXiv2023

Equivariant online predictions of non-stationary time series

We discuss the finite sample theoretical properties of online predictions in non-stationary time series under model misspecification. To analyze the theoretical predictive properties of statistical methods under this setting, we first define the Kullback-Leibler risk, in order to place the problem within a decision theoretic framework. Under this framework, we show that a specific class of dynamic models -- random walk dynamic linear models -- produce exact minimax predictive densities. We first show this result under Gaussian assumptions, then relax this assumption using semi-martingale processes. This result provides a theoretical baseline, under both non-stationary and stationary time series data, for which other models can be compared against. We extend the result to the synthesis of multiple predictive densities. Three topical applications in epidemiology, climatology, and economics, confirm and highlight our theoretical results.

math.ST↗

arXiv2023

Denoising Cosine Similarity: A Theory-Driven Approach for Efficient Representation Learning

Representation learning has been increasing its impact on the research and practice of machine learning, since it enables to learn representations that can apply to various downstream tasks efficiently. However, recent works pay little attention to the fact that real-world datasets used during the stage of representation learning are commonly contaminated by noise, which can degrade the quality of learned representations. This paper tackles the problem to learn robust representations against noise in a raw dataset. To this end, inspired by recent works on denoising and the success of the cosine-similarity-based objective functions in representation learning, we propose the denoising Cosine-Similarity (dCS) loss. The dCS loss is a modified cosine-similarity loss and incorporates a denoising property, which is supported by both our theoretical and empirical findings. To make the dCS loss implementable, we also construct the estimators of the dCS loss with statistical guarantees. Finally, we empirically show the efficiency of the dCS loss over the baseline objective functions in vision and speech domains.

stat.ML↗