arXiv subjects

Housen Li

Publications and source records attributed to Housen Li.

At least 19 recordsLinked to original sources

arXiv2026

Inferring Cooperativity From Pooled Measurements

In many modern experiments, latent interactions drive multicomponent stochastic systems, yet the data are available only as pooled measurements that obscure these dependencies. Whether such interactions can be identified and inferred from aggregate signals remains largely unexplored. Motivated by multi-channel electrophysiological recordings, we address this problem by introducing sum-dependent Markov chains, a class of finite-state continuous-time multivariate Markov processes whose transition rates encode interactions through the aggregate state. Under natural structural conditions, we establish identifiability of the latent dynamic parameters from the aggregate process. We define a cooperativity index that distinguishes positive cooperativity, negative cooperativity and independence, and construct its consistent estimators. For discretely and noisily observed pooled data, we develop likelihood-based inference through a hidden Markov model, address the associated embedding problem, and prove consistency and asymptotic normality. We further propose a stepdown test for cooperativity with asymptotic size control and power guarantees. Simulations and real-data analyses, demonstrate the scope and effectiveness of the methodology.

stat.ME↗

arXiv2025

Weak convergence of Bayes estimators under general loss functions

We investigate the asymptotic behavior of parametric Bayes estimators under a broad class of loss functions that extend beyond the classical translation-invariant setting. To this end, we develop a unified theoretical framework for loss functions exhibiting locally polynomial structure. This general theory encompasses important examples such as the squared Wasserstein distance, the Sinkhorn divergence and Stein discrepancies, which have gained prominence in modern statistical inference and machine learning. Building on the classical Bernstein--von Mises theorem, we establish sufficient conditions under which Bayes estimators inherit the posterior's asymptotic normality. As a by-product, we also derive conditions for the differentiability of Wasserstein-induced loss functions and provide new consistency results for Bayes estimators. Several examples and numerical experiments demonstrate the relevance and accuracy of the proposed methodology.

math.ST↗

arXiv2025

Central limit theorems for the eigenvalues of graph Laplacians on data clouds

Given i.i.d.\ samples $X_n =\{ x_1, \dots, x_n \}$ from a distribution supported on a low dimensional manifold ${M}$ embedded in Eucliden space, we consider the graph Laplacian operator $\Delta_n$ associated to an $\varepsilon$-proximity graph over $X_n$ and study the asymptotic fluctuations of its eigenvalues around their means. In particular, letting $\hat{\lambda}_l^\varepsilon$ denote the $l$-th eigenvalue of $\Delta_n$, and under suitable assumptions on the data generating model and on the rate of decay of $\varepsilon$, we prove that $\sqrt{n } (\hat{\lambda}_{l}^\varepsilon - \mathbb{E}[\hat{\lambda}_{l}^\varepsilon] )$ is asymptotically Gaussian with a variance that we can explicitly characterize. A formal argument allows us to interpret this asymptotic variance as the dissipation of a gradient flow of a suitable energy with respect to the Fisher-Rao geometry. This geometric interpretation allows us to give, in turn, a statistical interpretation of the asymptotic variance in terms of a Cramer-Rao lower bound for the estimation of the eigenvalues of certain weighted Laplace-Beltrami operator. The latter interpretation suggests a form of asymptotic statistical efficiency for the eigenvalues of the graph Laplacian. We also present CLTs for multiple eigenvalues and through several numerical experiments explore the validity of our results when some of the assumptions that we make in our theoretical analysis are relaxed.

stat.ML↗

arXiv2025

Covariance scanning for adaptively optimal change point detection in high-dimensional linear models

This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed by the sparsity of the covariance-weighted differential parameter. This form of "inherent sparsity" captures a delicate interplay between the covariance structure of the regressors and the change in regression coefficients on the detectability of a change point. Complementing the lower bounds, we introduce two covariance scanning-based methods, McScan and QcSan, which achieve minimax optimal performance (up to possible logarithmic factors) in the sparse and the dense regimes, respectively. In particular, QcScan is the first method shown to achieve consistency in the dense regime and further, we devise a combined procedure which is adaptively minimax optimal across sparse and dense regimes without the knowledge of the sparsity. Computationally, covariance scanning-based methods avoid costly computation of Lasso-type estimators and attain worst-case computation complexity that is linear in the dimension and sample size. Additionally, we consider the post-detection estimation of the differential parameter and the refinement of the change point estimator. Simulation studies support the theoretical findings and demonstrate the computational and statistical efficiency of the proposed covariance scanning methods.

math.ST↗

arXiv2025

Online jump and kink detection in segmented linear regression: Statistical optimality meets computational efficiency

We consider the problem of sequential (online) estimation of a single change point in a piecewise linear regression model under a Gaussian setup. We demonstrate that certain CUSUM-type statistics attain the minimax optimal rates for localizing the change point. Our minimax analysis unveils an interesting phase transition from a jump (discontinuity in function values) to a kink (a change in slope). Specifically, for a jump, the minimax rate is of order $\log (n) / n$ , whereas for a kink it scales as $(\log (n) / n)^{1/3}$, given that the sampling rate is of order $1/n$. We further introduce an online algorithm based on these detectors, which optimally identifies both a jump and a kink, and is able to distinguish between them. Notably, the algorithm operates with constant computational complexity and requires only constant memory per incoming sample. Finally, we evaluate the empirical performance of our method on both simulated and real-world data sets. An implementation is available in the R package FLOC on GitHub.

math.ST↗

arXiv2025

Adaptive monotonicity testing in sublinear time

Modern large-scale data analysis increasingly faces the challenge of achieving computational efficiency as well as statistical accuracy, as classical statistically efficient methods often fall short in the first regard. In the context of testing monotonicity of a regression function, we propose FOMT (Fast and Optimal Monotonicity Test), a novel methodology tailored to meet these dual demands. FOMT employs a sparse collection of local tests, strategically generated at random, to detect violations of monotonicity scattered throughout the domain of the regression function. This sparsity enables significant computational efficiency, achieving sublinear runtime in most cases, and quasilinear runtime (i.e., linear up to a log factor) in the worst case. In contrast, existing statistically optimal tests typically require at least quadratic runtime. FOMT's statistical accuracy is achieved through the precise calibration of these local tests and their effective combination, ensuring both sensitivity to violations and control over false positives. More precisely, we show that FOMT separates the null and alternative hypotheses at minimax optimal rates over H\"older function classes of smoothness order in $(0,2]$. Further, when the smoothness is unknown, we introduce an adaptive version of FOMT, based on a modified Lepskii principle, which attains statistical optimality and meanwhile maintains the same computational complexity as if the intrinsic smoothness were known. Extensive simulations confirm the competitiveness and effectiveness of both FOMT and its adaptive variant.

math.ST↗

arXiv2024

Distributional limits of graph cuts on discretized grids

Graph cuts are among the most prominent tools for clustering and classification analysis. While intensively studied from geometric and algorithmic perspectives, graph cut-based statistical inference still remains elusive to a certain extent. Distributional limits are fundamental in understanding and designing such statistical procedures on randomly sampled data. We provide explicit limiting distributions for balanced graph cuts in general on a fixed but arbitrary discretization. In particular, we show that Minimum Cut, Ratio Cut and Normalized Cut behave asymptotically as the minimum of Gaussians as sample size increases. Interestingly, our results reveal a dichotomy for Cheeger Cut: The limiting distribution of the optimal objective value is the minimum of Gaussians only when the optimal partition yields two sets of unequal volumes, while otherwise the limiting distribution is the minimum of a random mixture of Gaussians. Further, we show the bootstrap consistency for all types of graph cuts by utilizing the directional differentiability of cut functionals. We validate these theoretical findings by Monte Carlo experiments, and examine differences between the cuts and the dependency on the underlying distribution. Additionally, we expand our theoretical findings to the Xist algorithm, a computational surrogate of graph cuts recently proposed in Suchan, Li and Munk (arXiv, 2023), thus demonstrating the practical applicability of our findings e.g. in statistical tests.

math.ST↗

arXiv2024

Robust inference of cooperative behaviour of multiple ion channels in voltage-clamp recordings

Recent experimental studies have shed light on the intriguing possibility that ion channels exhibit cooperative behaviour. However, a comprehensive understanding of such cooperativity remains elusive, primarily due to limitations in measuring separately the response of each channel. Rather, only the superimposed channel response can be observed, challenging existing data analysis methods. To address this gap, we propose IDC (Idealisation, Discretisation, and Cooperativity inference), a robust statistical data analysis methodology that requires only voltage-clamp current recordings of an ensemble of ion channels. The framework of IDC enables us to integrate recent advancements in idealisation techniques and coupled Markov models. Further, in the cooperativity inference phase of IDC, we introduce a minimum distance estimator and establish its statistical guarantee in the form of asymptotic consistency. We demonstrate the effectiveness and robustness of IDC through extensive simulation studies. As an application, we investigate gramicidin D channels. Our findings reveal that these channels act independently, even at varying applied voltages during voltage-clamp experiments. An implementation of IDC is available from GitLab.

stat.ME↗

arXiv2024

Multiscale Quantile Regression with Local Error Control

For robust and efficient detection of change points, we introduce a novel methodology MUSCLE (Multiscale qUantile Segmentation Controlling Local Error) that partitions serial data into multiple segments, each sharing a common quantile. It leverages multiple tests for quantile changes over different scales and locations, and variational estimation. Unlike the often adopted global error control, MUSCLE focuses on local errors defined on individual segments, significantly improving detection power in finding change points. Meanwhile, due to the built-in model complexity penalty, it enjoys the finite sample guarantee that its false discovery rate (or the expected proportion of falsely detected change points) is upper bounded by its unique tuning parameter. Further, we obtain the consistency and the localization error rates in estimating change points, under mild signal-to-noise-ratio conditions. Both match (up to log factors) the minimax optimality results in the Gaussian setup. All theories hold under the only distributional assumption of serial independence. Incorporating the wavelet tree data structure, we develop an efficient dynamic programming algorithm for computing MUSCLE. Extensive simulations as well as real data applications in electrophysiology and geophysics demonstrate its competitiveness and effectiveness. An implementation via R package muscle is available on GitHub.

stat.ME↗

arXiv2024

Detection and inference of changes in high-dimensional linear regression with non-sparse structures

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised maximum likelihood-type estimation and then contrast them for change point detection. Contrary to this common practice, we show that the exact sparsity of neither regression parameters nor their differences, a.k.a.\ differential parameters, is necessary for consistency in multiple change point detection. In fact, both statistically and computationally, better efficiency is attained by a simple strategy that scans for large discrepancies in local covariance between the regressors and the response. We go a step further and propose a suite of tools for directly inferring about the differential parameters post-segmentation, which are applicable even when the regression parameters themselves are non-sparse. Theoretical investigations are conducted under general conditions permitting non-Gaussianity, temporal dependence and ultra-high dimensionality. Numerical results from simulated and macroeconomic datasets demonstrate the competitiveness and efficacy of the proposed methods. Implementation of all methods is provided in the R package \texttt{inferchange} on GitHub.

stat.ME↗

arXiv2023

A scalable clustering algorithm to approximate graph cuts

Due to their computational complexity, graph cuts for cluster detection and identification are used mostly in the form of convex relaxations. We propose to utilize the original graph cuts such as Ratio, Normalized or Cheeger Cut to detect clusters in weighted undirected graphs by restricting the graph cut minimization to $st$-MinCut partitions. Incorporating a vertex selection technique and restricting optimization to tightly connected clusters, we combine the efficient computability of $st$-MinCuts and the intrinsic properties of Gomory-Hu trees with the cut quality of the original graph cuts, leading to linear runtime in the number of vertices and quadratic in the number of edges. Already in simple scenarios, the resulting algorithm Xist is able to approximate graph cut values better empirically than spectral clustering or comparable algorithms, even for large network datasets. We showcase its applicability by segmenting images from cell biology and provide empirical studies of runtime and classification rate.

cs.DS↗

arXiv2023

Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models

Hidden Markov models (HMMs) are characterized by an unobservable Markov chain and an observable process -- a noisy version of the hidden chain. Decoding the original signal from the noisy observations is one of the main goals in nearly all HMM based data analyses. Existing decoding algorithms such as Viterbi and the pointwise maximum a posteriori (PMAP) algorithm have computational complexity at best linear in the length of the observed sequence, and sub-quadratic in the size of the state space of the hidden chain. We present Quick Adaptive Ternary Segmentation (QATS), a divide-and-conquer procedure with computational complexity polylogarithmic in the length of the sequence, and cubic in the size of the state space, hence particularly suited for large scale HMMs with relatively few states. It also suggests an effective way of data storage as specific cumulative sums. In essence, the estimated sequence of states sequentially maximizes local likelihood scores among all local paths with at most three segments, and is meanwhile admissible. The maximization is performed only approximately using an adaptive search procedure. Our simulations demonstrate the speedups offered by QATS in comparison to Viterbi and PMAP, along with a precision analysis. An implementation of QATS is in the R-package QATS on GitHub.

stat.ME↗

arXiv2023

Adaptive minimax optimality in statistical inverse problems via SOLIT -- Sharp Optimal Lepskii-Inspired Tuning

We consider statistical linear inverse problems in separable Hilbert spaces and filter-based reconstruction methods of the form $\hat f_\alpha = q_\alpha \left(T^*T\right)T^*Y$, where $Y$ is the available data, $T$ the forward operator, $\left(q_\alpha\right)_{\alpha \in \mathcal A}$ an ordered filter, and $\alpha > 0$ a regularization parameter. Whenever such a method is used in practice, $\alpha$ has to be appropriately chosen. Typically, the aim is to find or at least approximate the best possible $\alpha$ in the sense that mean squared error (MSE) $\mathbb E [\Vert \hat f_\alpha - f^\dagger\Vert^2]$ w.r.t.~the true solution $f^\dagger$ is minimized. In this paper, we introduce the Sharp Optimal Lepski\u{\i}-Inspired Tuning (SOLIT) method, which yields an a posteriori parameter choice rule ensuring adaptive minimax rates of convergence. It depends only on $Y$ and the noise level $\sigma$ as well as the operator $T$ and the filter $\left(q_\alpha\right)_{\alpha \in \mathcal A}$ and does not require any problem-dependent tuning of further parameters. We prove an oracle inequality for the corresponding MSE in a general setting and derive the rates of convergence in different scenarios. By a careful analysis we show that no other a posteriori parameter choice rule can yield a better performance in terms of the order of the convergence rate of the MSE. In particular, our results reveal that the typical understanding of Lepski\u\i-type methods in inverse problems leading to a loss of a log factor is wrong. In addition, the empirical performance of SOLIT is examined in simulations.

math.ST↗

arXiv2021

A Variational View on Statistical Multiscale Estimation

We present a unifying view on various statistical estimation techniques including penalization, variational and thresholding methods. These estimators will be analyzed in the context of statistical linear inverse problems including nonparametric and change point regression, and high dimensional linear models as examples. Our approach reveals many seemingly unrelated estimation schemes as special instances of a general class of variational multiscale estimators, named MIND (MultIscale Nemirovskii--Dantzig). These estimators result from minimizing certain regularization functionals under convex constraints that can be seen as multiple statistical tests for local hypotheses. For computational purposes, we recast MIND in terms of simpler unconstraint optimization problems via Lagrangian penalization as well as Fenchel duality. Performance of several MINDs is demonstrated on numerical examples.

stat.ME↗

arXiv2020

Variational Multiscale Nonparametric Regression: Algorithms and Implementation

Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denoising. We consider in particular certain variational multiscale estimators which are statistically optimal in minimax sense, yet computationally intensive. Such an estimator is computed as the minimiser of a smoothness functional (e.g., TV norm) over the class of all estimators such that none of its coefficients with respect to a given multiscale dictionary is statistically significant. The so obtained multiscale Nemirowski-Dantzig estimator (MIND) can incorporate any convex smoothness functional and combine it with a proper dictionary including wavelets, curvelets and shearlets. The computation of MIND in general requires to solve a high-dimensional constrained convex optimisation problem with a specific structure of the constraints induced by the statistical multiscale testing criterion. To solve this explicitly, we discuss three different algorithmic approaches: the Chambolle-Pock, ADMM and semismooth Newton algorithms. Algorithmic details and an explicit implementation is presented and the solutions are then compared numerically in a simulation study and on various test images. We thereby recommend the Chambolle-Pock algorithm in most cases for its fast convergence. We stress that our analysis can also be transferred to signal recovery and other denoising problems to recover more general objects whenever it is possible to borrow statistical strength from data patches of similar object structure.

stat.CO↗

arXiv2020

Optimistic search: Change point estimation for large-scale data via adaptive logarithmic queries

Change point estimation is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidates requires $O(n)$ evaluations of the gain function for an interval with $n$ observations. If each evaluation is computationally demanding (e.g. in high-dimensional models), this can become infeasible. Instead, we propose optimistic search methods with $O(\log n)$ evaluations exploiting specific structure of the gain function. Towards solid understanding of our strategy, we investigate in detail the $p$-dimensional Gaussian changing means setup, including high-dimensional scenarios. For some of our proposals, we prove asymptotic minimax optimality for detecting change points and derive their asymptotic localization rate. These rates (up to a possible log factor) are optimal for the univariate and multivariate scenarios, and are by far the fastest in the literature under the weakest possible detection condition on the signal-to-noise ratio in the high-dimensional scenario. Computationally, our proposed methodology has the worst case complexity of $O(np)$, which can be improved to be sublinear in $n$ if some a-priori knowledge on the length of the shortest segment is available. Our search strategies generalize far beyond the theoretically analyzed setup. We illustrate, as an example, massive computational speedup in change point detection for high-dimensional Gaussian graphical models.

stat.ME↗

arXiv2020

Seeded intervals and noise level estimation in change point detection: A discussion of Fryzlewicz (2020)

In this discussion, we compare the choice of seeded intervals and that of random intervals for change point segmentation from practical, statistical and computational perspectives. Furthermore, we investigate a novel estimator of the noise level, which improves many existing model selection procedures (including the steepest drop to low levels), particularly for challenging frequent change point scenarios with low signal-to-noise ratios.

stat.ME↗

arXiv2020

Seeded Binary Segmentation: A general methodology for fast and optimal change point detection

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of background intervals, called seeded intervals, in which single change points are searched. The final selection of change points based on the candidates from seeded intervals can be done in various ways, adapted to the problem at hand. Thus, seeded binary segmentation is easy to adapt to a wide range of change point detection problems, let that be univariate, multivariate or even high-dimensional. We consider the univariate Gaussian change in mean setup in detail. For this specific case we show that seeded binary segmentation leads to a near-linear time approach (i.e. linear up to a logarithmic factor) independent of the underlying number of change points. Furthermore, using appropriate selection methods, the methodology is shown to be asymptotically minimax optimal. While computationally more efficient, the finite sample estimation performance remains competitive compared to state of the art procedures. Moreover, we illustrate the methodology for high-dimensional settings with an inverse covariance change point detection problem where our proposal leads to massive computational gains while still exhibiting good statistical performance.

stat.ME↗