arXiv subjects

Daniel Y. Takahashi

Publications and source records attributed to Daniel Y. Takahashi.

7 recordsLinked to original sources

arXiv2026

SPIDER -- Stitched Power-spectra for Inferring Directed information flow from incomplete and asynchronous Experimental Recordings

Mapping the directed flow of information between brain regions -- their effective connectivity -- is central to understanding brain function, yet large-scale recordings sample only a fraction of the brain at a time: sessions, animals, and laboratories cover different, partially overlapping regions, usually without a shared temporal reference. Established directed-connectivity methods (Granger causality, dynamic causal modeling, partial directed coherence, PDC) require all regions to be recorded simultaneously and with a common clock. We introduce SPIDER, a non-parametric, frequency-domain framework that recovers directed information flow from such incomplete, asynchronous recordings: it stitches local power-spectral estimates from overlapping channel subsets into a global spectral matrix and obtains frequency-resolved directed interactions by canonical spectral factorization and PDC, without temporal alignment, while nuclear-norm completion fills in never-co-observed region pairs. With consistency guarantees, we validate SPIDER on simulations, two-photon calcium imaging, and the International Brain Laboratory Neuropixels dataset, recovering directed flow among 50 areas from 43 sessions in 12 laboratories never recorded together. Beyond validation, SPIDER reveals what no single recording can: brain-wide spontaneous flow is largely recurrent, but in the theta band it forms a significant feedforward hierarchy with the hippocampal formation at its source. Applied to resting human intracranial EEG (43 patients, non-overlapping coverage), it recovers the same theta-band hierarchy across species and modality. SPIDER makes whole-brain effective-connectivity analysis tractable for multi-session, multi-animal datasets previously incompatible with directed-flow inference.

q-bio.NC↗

arXiv2025

hdMTD: An R Package for High-Dimensional Mixture Transition Distribution Models

Several natural phenomena exhibit long-range conditional dependencies. High-order mixture transition distribution (MTD) are parsimonious non-parametric models to study these phenomena. An MTD is a Markov chain in which the transition probabilities are expressed as a convex combination of lower-order conditional distributions. Despite their generality, inference for MTD models has traditionally been limited by the need to estimate high-dimensional joint distributions. In particular, for a sample of size n, the feasible order d of the MTD is typically restricted to d approximately O(log n). To overcome this limitation, Ost and Takahashi (2023) recently introduced a computationally efficient non-parametric inference method that identifies the relevant lags in high-order MTD models, even when d is approximately O(n), provided that the set of relevant lags is sparse. In this article, we introduce hdMTD, an R package allowing us to estimate parameters of such high-dimensional Markovian models. Given a sample from an MTD chain, hdMTD can retrieve the relevant past set using the BIC algorithm or the forward stepwise and cut algorithm described in Ost and Takahashi (2023). The package also computes the maximum likelihood estimate for transition probabilities and estimates high-order MTD parameters through the expectation-maximization algorithm. Additionally, hdMTD also allows for simulating an MTD chain from its stationary invariant distribution using the perfect (exact) sampling algorithm, enabling Monte Carlo simulation of the model. We illustrate the package's capabilities through simulated data and a real-world application involving temperature records from Brazil.

stat.ME↗

arXiv2025

Self-switching random walks on Erdös-Rényi random graphs feel the phase transition

We study random walks on Erdös-Rényi random graphs in which, every time the random walk returns to the starting point, first an edge probability is independently sampled according to a priori measure $μ$, and then an Erdös-Rényi random graph is sampled according to that edge probability. When the edge probability $p$ does not depend on the size of the graph $n$ (dense case), we show that the proportion of time the random walk spends on different values of $p$ -- {\it occupation measure} -- converges to the a priori measure $μ$ as $n$ goes to infinity. More interestingly, when $p=λ/n$ (sparse case), we show that the occupation measure converges to a limiting measure with a density that is a function of the survival probability of a Poisson branching process. This limiting measure is supported on the supercritial values for the Erdös-Rényi random graphs, showing that self-witching random walks can detect the phase transition.

math.PR↗

arXiv2021

Mixing rates for potentials of non-summable variations

Mixing rates and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. In this paper, we exhibit upper bounds for these quantities in the case of dynamics defined by potentials with square summable variations. We obtain these bounds as corollaries of a new block coupling inequality between pair of dynamics starting with different histories. As applications of our results, we prove a new weak invariance principle and a Chernoff-type inequality.

math.DS↗

arXiv2016

Sharp oracle inequalities and slope heuristic for specification probabilities estimation in discrete random fields

We study the problem of estimating the one-point specification probabilities in non-necessary finite discrete random fields from partially observed independent samples. Our procedures are based on model selection by minimization of a penalized empirical criterion. The selected estimators satisfy sharp oracle inequalities in $L_2$-risk. We also obtain theoretical results on the slope heuristic for this problem, justifying the slope algorithm to calibrate the leading constant in the penalty. The practical performances of our methods are investigated in two simulation studies. We illustrate the usefulness of our approach by applying the methods to a multi-unit neuronal data from a rat hippocampus.

math.ST↗

arXiv2015

Consolidating a Link Centered Neural Connectivity Framework with Directed Transfer Function Asymptotics

We present a unified mathematical derivation of the asymptotic behaviour of three of the main forms of \textit{directed transfer function} (DTF) complementing recent partial directed coherence (PDC) results \cite{Baccala2013}. Based on these results and numerical examples we argue for a new directed `link' centered neural connectivity framework to replace the widespread correlation based effective/functional network concepts so that directed network influences between structures become classified as to whether links are \textit{active} in a \textit{direct} or in an \textit{indirect} way thereby leading to the new notions of \textit{Granger connectivity} and \textit{Granger influenciability} which are more descriptive than speaking of Granger causality alone.

q-bio.NC↗

arXiv2013

A statistical test to identify differences in clustering structures

Statistical inference on functional magnetic resonance imaging (fMRI) data is an important task in brain imaging. One major hypothesis is that the presence or not of a psychiatric disorder can be explained by the differential clustering of neurons in the brain. In view of this fact, it is clearly of interest to address the question of whether the properties of the clusters have changed between groups of patients and controls. The normal method of approaching group differences in brain imaging is to carry out a voxel-wise univariate analysis for a difference between the mean group responses using an appropriate test (e.g. a t-test) and to assemble the resulting "significantly different voxels" into clusters, testing again at cluster level. In this approach of course, the primary voxel-level test is blind to any cluster structure. Direct assessments of differences between groups (or reproducibility within groups) at the cluster level have been rare in brain imaging. For this reason, we introduce a novel statistical test called ANOCVA - ANalysis Of Cluster structure Variability, which statistically tests whether two or more populations are equally clustered using specific features. The proposed method allows us to compare the clustering structure of multiple groups simultaneously, and also to identify features that contribute to the differential clustering. We illustrate the performance of ANOCVA through simulations and an application to an fMRI data set composed of children with ADHD and controls. Results show that there are several differences in the brain's clustering structure between them, corroborating the hypothesis in the literature. Furthermore, we identified some brain regions previously not described, generating new hypothesis to be tested empirically.

stat.ME↗