We study online change point detection problems under the constraint of local differential privacy (LDP) where, in particular, the statistician does not have access to the raw data. As a concrete problem, we study a multivariate nonparametric regression problem. At each time point t, the raw data are assumed to be of the form (Xt,Yt), where Xt is a d-dimensional feature vector and Yt is a response variable. Our primary aim is to detect changes in the regression function mt(x) = E(Yt|Xt = x) as soon as the change occurs. We provide algorithms which respect the LDP constraint, which control the false alarm probability, and which detect changes with a minimal (minimax rate-optimal) delay. To quantify the cost of privacy, we also present the optimal rate in the benchmark, non-private setting. These non-private results are also new to the literature and thus are interesting per se. In addition, we study the univariate mean online change point detection problem, under privacy constraints. This serves as the blueprint of studying more complicated private change point detection problems.

The objective of change point detection (CPD) is to detect significant and abrupt changes in the dynamics of the underlying system of interest through multivariate time series observations. In this work, we develop and analyze an algorithm for CPD that is inspired by a variant of the classical singular spectrum analysis (SSA) approach for time series by combining it with the classical cumulative sum (CUSUM) statistic from sequential hypothesis testing. In particular, we model the underlying dynamics of multivariate time series observations through the spatio-temporal model introduced recently in the multivariate SSA (mSSA) literature.

Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the other hand, probabilistic ``white box'' models, though interpretable, often suffer from a significant performance gap when compared to neural networks. To address this, we propose a novel quantum physics-based ``white box'' method that offers both accurate uncertainty quantification and enhanced interpretability. By mapping the kernel mean embedding (KME) of a time series data vector to a reproducing kernel Hilbert space (RKHS), we construct a tensor network-inspired 1D spin chain Hamiltonian, with the KME as one of its eigen-functions or eigen-modes. We then solve the associated Schr{ö}dinger equation and apply perturbation theory to quantify uncertainty, thereby improving the interpretability of tasks performed with the quantum tensor network-based model. We demonstrate the effectiveness of this methodology, compared to state-of-the-art ``white box" models, in change point detection and time series clustering, providing insights into the uncertainties associated with decision-making throughout the process.

Hierarchical Reinforcement Learning (HRL) enhances the scalability of decision-making in long-horizon tasks by introducing temporal abstraction through options-policies that span multiple timesteps. Despite its theoretical appeal, the practical implementation of HRL suffers from the challenge of autonomously discovering semantically meaningful subgoals and learning optimal option termination boundaries. This paper introduces a novel architecture that integrates a self-supervised, Transformer-based Change Point Detection (CPD) module into the Option-Critic framework, enabling adaptive segmentation of state trajectories and the discovery of options. The CPD module is trained using heuristic pseudo-labels derived from intrinsic signals to infer latent shifts in environment dynamics without external supervision. These inferred change-points are leveraged in three critical ways: (i) to serve as supervisory signals for stabilizing termination function gradients, (ii) to pretrain intra-option policies via segment-wise behavioral cloning, and (iii) to enforce functional specialization through inter-option divergence penalties over CPD-defined state partitions. The overall optimization objective enhances the standard actor-critic loss using structure-aware auxiliary losses. In our framework, option discovery arises naturally as CPD-defined trajectory segments are mapped to distinct intra-option policies, enabling the agent to autonomously partition its behavior into reusable, semantically meaningful skills. Experiments on the Four-Rooms and Pinball tasks demonstrate that CPD-guided agents exhibit accelerated convergence, higher cumulative returns, and significantly improved option specialization. These findings confirm that integrating structural priors via change-point segmentation leads to more interpretable, sample-efficient, and robust hierarchical policies in complex environments.

We propose a framework for online Change Point Detection (CPD) from multi-entity, multivariate time series data, motivated by applications in crowd monitoring where traditional sensing methods (e.g., video surveillance) may be infeasible. Our approach addresses the challenge of detecting system-wide behavioral shifts in complex, dynamic environments where the number and behavior of individual entities may be uncertain or evolve. We introduce the concept of Individual Deviation from Normality (IDfN), computed via a reconstruction-error-based autoencoder trained on normal behavior. We aggregate these individual deviations using mean, variance, and Kernel Density Estimates (KDE) to yield a System-Wide Anomaly Score (SWAS). To detect persistent or abrupt changes, we apply statistical deviation metrics and the Cumulative Sum (CUSUM) technique to these scores. Our unsupervised approach eliminates the need for labeled data or feature extraction, enabling real-time operation on streaming input. Evaluations on both synthetic datasets and crowd simulations, explicitly designed for anomaly detection in group behaviors, demonstrate that our method accurately detects significant system-level changes, offering a scalable and privacy-preserving solution for monitoring complex multi-agent systems. In addition to this methodological contribution, we introduce new, challenging multi-entity multivariate time series datasets generated from crowd simulations in Unity and coupled nonlinear oscillators. To the best of our knowledge, there is currently no publicly available dataset of this type designed explicitly to evaluate CPD in complex collective and interactive systems, highlighting an essential gap that our work addresses.

In this paper we are concerned with localizing the change points in a high-dimensional BTL model with piece-wise constant parameters.

--Change Point Detection (CPD) aims to identify moments of abrupt distribution shifts in data streams. Real-world high-dimensional CPD remains challenging due to data pattern complexity and violation of common assumptions. Resorting to standalone deep neural networks, the current state-of-the-art detectors have yet to achieve perfect quality. Concurrently, ensembling provides more robust solutions, boosting the performance. In this paper, we investigate ensembles of deep change point detectors and realize that standard prediction aggregation techniques, e.g., averaging, are suboptimal and fail to account for problem peculiarities. Alternatively, we introduce WW Aggr -- a novel task-specific method of ensemble aggregation based on the Wasserstein distance. Our procedure is versatile, working effectively with various ensembles of deep CPD models. Moreover, unlike existing solutions, we practically lift a long-standing problem of the decision threshold selection for CPD. Change Point Detection (CPD) addresses the challenge of precise identification of the moments when some statistical properties of data distribution undergo alterations. Such a problem emerges in various real-world scenarios: manufacturing process monitoring [1, 2], server logs [3], financial data analysis [4, 5], or video surveillance [6].