arXiv subjects

Gaetano Romano

Publications and source records attributed to Gaetano Romano.

9 recordsLinked to original sources

arXiv2026

focus and focus-cpt: Fast Online Changepoint Detection in R and Python

We present an R and Python package for fast online changepoint detection in univariate and multivariate data streams for a variety of models. The package implements the focus family of algorithms, which compute the Generalised Likelihood Ratio test for a single changepoint exactly and efficiently, with a per-iteration cost of approximately $\log(n)^d$ for a d-dimensional sequence, without introducing approximations. This is achieved by exploiting a connection between the location of the changepoint candidates and the geometry of the data. The package supports a broad range of models from the natural exponential family, including Gaussian, Poisson, Binomial, Exponential and Gamma distributions, as well as a non-parametric detector based on the empirical cumulative distribution function and a detector for autoregressive data.

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arXiv2026

An Efficient Likelihood Ratio Test for Online Changepoint Detection in the Presence of Autocorrelation

Changepoint detection methods have seen considerable development in recent years, with online algorithms capable of identifying structural changes in streaming data in near real time. However, the majority of existing methods are designed under the assumption of IID observations, rendering them susceptible to either more false positives or longer detection delays when applied to data exhibiting temporal dependence, a common feature of many real-world data streams. In this article, we extend the generalised likelihood-ratio (GLR) statistic to autoregressive processes of order $p$, and adapt the focus algorithm to develop a computationally efficient online change detector. The resulting AR($p$)-focus algorithm achieves an average computational cost of $\mathcal{O}(\log n)$ per iteration, making it suitable for high-frequency data streams. Through simulation studies, the proposed approach is seen achieving greater detection power than IID-based tests when the underlying data exhibit temporal correlation. We further illustrate the practical utility of AR($p$)-focus through an application to a real-world telecommunications dataset.

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arXiv2026

Exact Multiple Change-Point Detection Via Smallest Valid Partitioning

We introduce smallest valid partitioning (SVP), a segmentation method for multiple change-point detection in time-series. SVP relies on a local notion of segment validity: a candidate segment is retained only if it passes a user-chosen validity test (e.g., a single change-point test). From the collection of valid segments, we propose a coherent aggregation procedure that constructs a global segmentation which is the exact solution of an optimization problem. Our main contribution is the use of a lexicographic order for the optimization problem that prioritizes parsimony. We analyze the computational complexity of the resulting procedure, which ranges from linear to cubic time depending on the chosen cost and validity functions, the data regime and the number of detected changes. Finally, we assess the quality of SVP through comparisons with standard optimal partitioning algorithms, showing that SVP yields competitive segmentations while explicitly enforcing segment validity. The flexibility of SVP makes it applicable to a broad class of problems; as an illustration, we demonstrate robust change-point detection by encoding robustness in the validity criterion.

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arXiv2023

Online Multivariate Changepoint Detection: Leveraging Links With Computational Geometry

The increasing volume of data streams poses significant computational challenges for detecting changepoints online. Likelihood-based methods are effective, but a naive sequential implementation becomes impractical online due to high computational costs. We develop an online algorithm that exactly calculates the likelihood ratio test for a single changepoint in $p$-dimensional data streams by leveraging a fascinating connection with computational geometry. This connection straightforwardly allows us to exactly recover sparse likelihood ratio statistics: that is assuming only a subset of the dimensions are changing. Our algorithm is straightforward, fast, and apparently quasi-linear. A dyadic variant of our algorithm is provably quasi-linear, being $\mathcal{O}(n\log(n)^{p+1})$ for $n$ data points and $p$ less than $3$, but slower in practice. These algorithms are computationally impractical when $p$ is larger than $5$, and we provide an approximate algorithm suitable for such $p$ which is $\mathcal{O}(np\log(n)^{\tilde{p}+1}), $ for some user-specified $\tilde{p} \leq 5$. We derive statistical guarantees for the proposed procedures in the Gaussian case, and confirm the good computational and statistical performance, and usefulness, of the algorithms on both empirical data and NBA data.

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arXiv2023

A Constant-per-Iteration Likelihood Ratio Test for Online Changepoint Detection for Exponential Family Models

Online changepoint detection algorithms that are based on likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time $T$, it involves considering $O(T)$ possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to $O(\log T)$. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time $T$ to approximately $\log T$. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately $\log T$ locations at iteration $T$. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.

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arXiv2023

A Log-Linear Non-Parametric Online Changepoint Detection Algorithm based on Functional Pruning

Online changepoint detection aims to detect anomalies and changes in real-time in high-frequency data streams, sometimes with limited available computational resources. This is an important task that is rooted in many real-world applications, including and not limited to cybersecurity, medicine and astrophysics. While fast and efficient online algorithms have been recently introduced, these rely on parametric assumptions which are often violated in practical applications. Motivated by data streams from the telecommunications sector, we build a flexible nonparametric approach to detect a change in the distribution of a sequence. Our procedure, NP-FOCuS, builds a sequential likelihood ratio test for a change in a set of points of the empirical cumulative density function of our data. This is achieved by keeping track of the number of observations above or below those points. Thanks to functional pruning ideas, NP-FOCuS has a computational cost that is log-linear in the number of observations and is suitable for high-frequency data streams. In terms of detection power, NP-FOCuS is seen to outperform current nonparametric online changepoint techniques in a variety of settings. We demonstrate the utility of the procedure on both simulated and real data.

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arXiv2022

Fast Online Changepoint Detection via Functional Pruning CUSUM statistics

Many modern applications of online changepoint detection require the ability to process high-frequency observations, sometimes with limited available computational resources. Online algorithms for detecting a change in mean often involve using a moving window, or specifying the expected size of change. Such choices affect which changes the algorithms have most power to detect. We introduce an algorithm, Functional Online CuSUM (FOCuS), which is equivalent to running these earlier methods simultaneously for all sizes of window, or all possible values for the size of change. Our theoretical results give tight bounds on the expected computational cost per iteration of FOCuS, with this being logarithmic in the number of observations. We show how FOCuS can be applied to a number of different change in mean scenarios, and demonstrate its practical utility through its state-of-the art performance at detecting anomalous behaviour in computer server data.

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arXiv2022

gfpop: an R Package for Univariate Graph-Constrained Change-Point Detection

In a world with data that change rapidly and abruptly, it is important to detect those changes accurately. In this paper we describe an R package implementing a generalized version of an algorithm recently proposed by Hocking et al. [2020] for penalized maximum likelihood inference of constrained multiple change-point models. This algorithm can be used to pinpoint the precise locations of abrupt changes in large data sequences. There are many application domains for such models, such as medicine, neuroscience or genomics. Often, practitioners have prior knowledge about the changes they are looking for. For example in genomic data, biologists sometimes expect peaks: up changes followed by down changes. Taking advantage of such prior information can substantially improve the accuracy with which we can detect and estimate changes. Hocking et al. [2020] described a graph framework to encode many examples of such prior information and a generic algorithm to infer the optimal model parameters, but implemented the algorithm for just a single scenario. We present the gfpop package that implements the algorithm in a generic manner in R/C++. gfpop works for a user-defined graph that can encode prior assumptions about the types of change that are possible and implements several loss functions (Gauss, Poisson, binomial, biweight and Huber). We then illustrate the use of gfpop on isotonic simulations and several applications in biology. For a number of graphs the algorithm runs in a matter of seconds or minutes for 10^5 data points.

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arXiv2020

Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise

Whilst there are a plethora of algorithms for detecting changes in mean in univariate time-series, almost all struggle in real applications where there is autocorrelated noise or where the mean fluctuates locally between the abrupt changes that one wishes to detect. In these cases, default implementations, which are often based on assumptions of a constant mean between changes and independent noise, can lead to substantial over-estimation of the number of changes. We propose a principled approach to detect such abrupt changes that models local fluctuations as a random walk process and autocorrelated noise via an AR(1) process. We then estimate the number and location of changepoints by minimising a penalised cost based on this model. We develop a novel and efficient dynamic programming algorithm, DeCAFS, that can solve this minimisation problem; despite the additional challenge of dependence across segments, due to the autocorrelated noise, which makes existing algorithms inapplicable. Theory and empirical results show that our approach has greater power at detecting abrupt changes than existing approaches. We apply our method to measuring gene expression levels in bacteria.

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