arXiv subjects

Giorgio Micali

Publications and source records attributed to Giorgio Micali.

6 recordsLinked to original sources

arXiv2026

Central limit theorems for the outputs of fully convolutional neural networks with time series input

Deep learning is widely deployed for time series learning tasks such as classification and forecasting. Despite the empirical successes, only little theory has been developed so far in the time series context. In this work, we prove that if the network inputs are generated from short-range dependent linear processes, the outputs of fully convolutional neural networks (FCNs) with global average pooling (GAP) are asymptotically Gaussian and the limit is attained if the length of the observed time series tends to infinity. The proof leverages existing tools from the theoretical time series literature. Based on our theory, we propose a generalization of the GAP layer by considering a global weighted pooling step with slowly varying, learnable coefficients.

stat.ME↗

arXiv2026

Ordinal Patterns Based Testing of Spatial Independence in Irregular Spatial Structures

We propose a nonparametric test of spatial independence for data observed on irregular, non-lattice point clouds $\mathcal{V}_{n}\subset\mathbb{R}^{2}$. For each location $v\in\mathcal{V}_{n}$, we encode the local spatial configuration through the ordinal pattern of the $m$ nearest-neighbour observations, obtaining a symbolic representation that is invariant under strictly monotone transformations and robust to outliers. Under the null hypothesis of spatial independence, the local ordinal patterns are i.i.d.\ and uniformly distributed over the symmetric group $\mathcal{S}_{m}$, regardless of the unknown marginal distribution $F$. We exploit this characterisation to construct a test statistic $L_{n}$ based on the additive log-ratio (ALR) transformation of the empirical ordinal-pattern frequencies. Invoking a central limit theorem for graph-dependent processes under a graph-based $\alpha$-mixing condition, we establish that $L_{n}$ converges in distribution to a $\chi^{2}_{m!-1}$ random variable, yielding an asymptotically pivotal procedure with no nuisance parameters. An extensive Monte Carlo study confirms that the $\chi^{2}_{m!-1}$ approximation is accurate already at moderate sample sizes, that the test controls size at the nominal level, and that power increases monotonically with the strength of spatial dependence. Notably, the test detects dependence in both linear and nonlinearly transformed spatial autoregressive models, illustrating the robustness that is characteristic of ordinal-pattern methods. Our framework extends the spatial ordinal-pattern testing paradigm from regular lattices to general spatial supports, opening the door to ordinal-pattern inference in the many applied settings where observations are irregularly located.

stat.ME↗

arXiv2026

Symmetry Testing in Time Series using Ordinal Patterns: A U-Statistic Approach

We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides a unified framework applicable to arbitrary symmetry tests. We establish asymptotic results for the resulting test statistics under a broad class of stationary processes. Comprehensive experiments on both synthetic and real data demonstrate that the proposed test achieves high sensitivity to structural asymmetries while remaining fully data-driven and computationally efficient.

math.ST↗

arXiv2026

Secure Change-Point Detection for Time Series under Homomorphic Encryption

We introduce the first method for change-point detection on encrypted time series. Our approach employs the CKKS homomorphic encryption scheme to detect shifts in statistical properties (e.g., mean, variance, frequency) without ever decrypting the data. Unlike solutions based on differential privacy, which degrade accuracy through noise injection, our solution preserves utility comparable to plaintext baselines. We assess its performance through experiments on both synthetic datasets and real-world time series from healthcare and network monitoring. Notably, our approach can process one million points within 3 minutes.

cs.CR↗

arXiv2025

Ordinal Patterns Based Change Points Detection

The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of the time series. In this work, we prove the asymptotic normality of the relative frequency of ordinal patterns for time series with linear increments. Moreover, we apply ordinal patterns to detect changes in the distribution of a time series.

math.ST↗

arXiv2024

Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization

This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem whose solution corresponds to a distribution minimizing the difference between answers to the linear queries based on the true distribution and answers from a differentially private distribution. Against this background, we establish two new algorithms for corresponding differentially private data release: the first is based on the differentially private Frank-Wolfe method, the second combines randomized smoothing with stochastic convex optimization techniques for a solution to the saddle-point problem. While previous works assess the accuracy of differentially private algorithms with reference to the empirical data distribution, a key contribution of our work is a more natural evaluation of the proposed algorithms' accuracy with reference to the true data-generating distribution.

stat.ME↗