arXiv subjects

David Campos

Publications and source records attributed to David Campos.

12 recordsLinked to original sources

arXiv2026

Markov property and path regularity for the solutions to SPDEs driven by cylindrical-martingale valued measures

In this paper we prove the Markov property for the solution to stochastic partial differential equations driven by a cylindrical orthogonal martingale-valued measure. We assume our coefficients are time-dependent and satisfy some growth and Lipschitz conditions. We also prove that for time-independent coefficients and under mild assumptions on the cylindrical orthogonal martingale-valued measure, the solutions to our stochastic partial differential equations are Feller. Finally, in the case that the $C_{0}$-semigroup is quasi-contraction, we show that the solution to our stochastic partial differential equation possesses a c\`adl\`ag version.

math.PR↗

arXiv2026

TimeBlocks: Foundational and Continual Time-Series Blockbase -- Extended Version

The ongoing digitization has led to a proliferation of time-series data streams that monitor a variety of processes, from which valuable insights may be obtained. Further, the emergence of successful foundational language models begs the question of whether it is possible to achieve time-series models with the foundational properties of handling multiple tasks, while being sufficiently lightweight to allow real-time data stream processing. Existing foundational time-series models are often large and only effective in offline settings without stringent time and computational constraints, and where repeated model calibration is not needed. However, when applied to data streams, these models are ineffective due to their size and lack of support for continual calibration, which compromise their ability to deliver accurate real-time responses, their durability, and their deployability in hardware-limited settings. We propose TimeBlocks to enable versatile time-series processing by facilitating the efficient building of lightweight models suitable for multiple tasks under variable conditions. In particular, the method maintains a pool of interchangeable and modular model blocks that can be used to construct new time-series models. When presented with specific time-series data, a routing strategy iteratively selects the most suitable blocks to construct a lightweight and accurate model for the data. We equip TimeBlocks with a method called StreamCore to build a representative small subset of the data stream, which preserves a guaranteed approximation of the stream over time, enabling continual model calibration. An experimental study on multiple data sets and covering multiple tasks shows that TimeBlocks enables to build models capable of outperforming existing baselines.

cs.LG↗

arXiv2024

Estimation of Psychosocial Work Environment Exposures Through Video Object Detection. Proof of Concept Using CCTV Footage

This paper examines the use of computer vision algorithms to estimate aspects of the psychosocial work environment using CCTV footage. We present a proof of concept for a methodology that detects and tracks people in video footage and estimates interactions between customers and employees by estimating their poses and calculating the duration of their encounters. We propose a pipeline that combines existing object detection and tracking algorithms (YOLOv8 and DeepSORT) with pose estimation algorithms (BlazePose) to estimate the number of customers and employees in the footage as well as the duration of their encounters. We use a simple rule-based approach to classify the interactions as positive, neutral or negative based on three different criteria: distance, duration and pose. The proposed methodology is tested on a small dataset of CCTV footage. While the data is quite limited in particular with respect to the quality of the footage, we have chosen this case as it represents a typical setting where the method could be applied. The results show that the object detection and tracking part of the pipeline has a reasonable performance on the dataset with a high degree of recall and reasonable accuracy. At this stage, the pose estimation is still limited to fully detect the type of interactions due to difficulties in tracking employees in the footage. We conclude that the method is a promising alternative to self-reported measures of the psychosocial work environment and could be used in future studies to obtain external observations of the work environment.

cs.CV↗

arXiv2024

It\^o's Formula for It\^{o} processes defined with respect to a cylindrical-martingale valued measure

Using the authors' recently developed stochastic integration [Stoch PDE: Anal Comp, 2024], we prove an It\^{o} formula for Hilbert space-valued It\^{o} processes defined with respect to a cylindrical martingale-valued measure. We develop some tools from stochastic analysis, as are the predictable and optional quadratic variation of a stochastic integral, the continuous and purely discontinuous parts of an integral process, and a Riemann representation formula. As an application of our It\^{o} formula, we prove a Burkholder inequality for the stochastic integral defined with respect to a cylindrical martingale-valued measure. Finally, we derive It\^{o} formulas for Hilbert space-valued martingale-valued measures and for cylindrical square integrable martingales.

math.PR↗

arXiv2024

QCore: Data-Efficient, On-Device Continual Calibration for Quantized Models -- Extended Version

We are witnessing an increasing availability of streaming data that may contain valuable information on the underlying processes. It is thus attractive to be able to deploy machine learning models on edge devices near sensors such that decisions can be made instantaneously, rather than first having to transmit incoming data to servers. To enable deployment on edge devices with limited storage and computational capabilities, the full-precision parameters in standard models can be quantized to use fewer bits. The resulting quantized models are then calibrated using back-propagation and full training data to ensure accuracy. This one-time calibration works for deployments in static environments. However, model deployment in dynamic edge environments call for continual calibration to adaptively adjust quantized models to fit new incoming data, which may have different distributions. The first difficulty in enabling continual calibration on the edge is that the full training data may be too large and thus not always available on edge devices. The second difficulty is that the use of back-propagation on the edge for repeated calibration is too expensive. We propose QCore to enable continual calibration on the edge. First, it compresses the full training data into a small subset to enable effective calibration of quantized models with different bit-widths. We also propose means of updating the subset when new streaming data arrives to reflect changes in the environment, while not forgetting earlier training data. Second, we propose a small bit-flipping network that works with the subset to update quantized model parameters, thus enabling efficient continual calibration without back-propagation. An experimental study, conducted with real-world data in a continual learning setting, offers insight into the properties of QCore and shows that it is capable of outperforming strong baseline methods.

cs.LG↗

arXiv2023

Riesz spaces of signed charges on semi-rings

A constructive definition of the supremum of a family of set functions is exploited in the context of Riesz spaces of signed measures and finitely additive functions (signed charges) on semi-rings. We explore applications, particularly to establish a Jordan decomposition for signed charges on semi-rings, whether the structure of Riesz space is present or not.

math.FA↗

arXiv2023

Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs

We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (2016), to the case of cylindrical martingale-valued measures that are allowed to have discontinuous paths (this is carried out within the context of separable Banach spaces). Our theory of stochastic integration is applied to address the existence and uniqueness of solutions to stochastic partial differential equations in Hilbert spaces.

math.PR↗

arXiv2023

LightTS: Lightweight Time Series Classification with Adaptive Ensemble Distillation -- Extended Version

Due to the sweeping digitalization of processes, increasingly vast amounts of time series data are being produced. Accurate classification of such time series facilitates decision making in multiple domains. State-of-the-art classification accuracy is often achieved by ensemble learning where results are synthesized from multiple base models. This characteristic implies that ensemble learning needs substantial computing resources, preventing their use in resource-limited environments, such as in edge devices. To extend the applicability of ensemble learning, we propose the LightTS framework that compresses large ensembles into lightweight models while ensuring competitive accuracy. First, we propose adaptive ensemble distillation that assigns adaptive weights to different base models such that their varying classification capabilities contribute purposefully to the training of the lightweight model. Second, we propose means of identifying Pareto optimal settings w.r.t. model accuracy and model size, thus enabling users with a space budget to select the most accurate lightweight model. We report on experiments using 128 real-world time series sets and different types of base models that justify key decisions in the design of LightTS and provide evidence that LightTS is able to outperform competitors.

cs.LG↗

arXiv2021

Unsupervised Time Series Outlier Detection with Diversity-Driven Convolutional Ensembles -- Extended Version

With the sweeping digitalization of societal, medical, industrial, and scientific processes, sensing technologies are being deployed that produce increasing volumes of time series data, thus fueling a plethora of new or improved applications. In this setting, outlier detection is frequently important, and while solutions based on neural networks exist, they leave room for improvement in terms of both accuracy and efficiency. With the objective of achieving such improvements, we propose a diversity-driven, convolutional ensemble. To improve accuracy, the ensemble employs multiple basic outlier detection models built on convolutional sequence-to-sequence autoencoders that can capture temporal dependencies in time series. Further, a novel diversity-driven training method maintains diversity among the basic models, with the aim of improving the ensemble's accuracy. To improve efficiency, the approach enables a high degree of parallelism during training. In addition, it is able to transfer some model parameters from one basic model to another, which reduces training time. We report on extensive experiments using real-world multivariate time series that offer insight into the design choices underlying the new approach and offer evidence that it is capable of improved accuracy and efficiency. This is an extended version of "Unsupervised Time Series Outlier Detection with Diversity-Driven Convolutional Ensembles", to appear in PVLDB 2022.

cs.LG↗

arXiv2015

Asymptotic expansion of the invariant measure for ballistic random walk in the low disorder regime

We consider a random walk in random environment in the low disorder regime on $\mathbb Z^d$. That is, the probability that the random walk jumps from a site $x$ to a nearest neighboring site $x+e$ is given by $p(e)+εξ(x,e)$, where $p(e)$ is deterministic, $\{\{ξ(x,e):|e|_1=1\}:x\in\mathbb Z^d\}$ are i.i.d. and $ε>0$ is a parameter which is eventually chosen small enough. We establish an asymptotic expansion in $ε$ for the invariant measure of the environmental process whenever a ballisticity condition is satisfied. As an application of our expansion, we derive a numerical expression up to first order in $ε$ for the invariant measure of random perturbations of the simple symmetric random walk in dimensions $d=2$.

math.PR↗

arXiv2014

Ellipticity criteria for ballistic behavior of random walks in random environment

We introduce ellipticity criteria for random walks in i.i.d. random environments under which we can extend the ballisticity conditions of Sznitman's and the polynomial effective criteria of Berger, Drewitz and Ramirez originally defined for uniformly elliptic random walks. We prove under them the equivalence of Sznitman's (T') condition with the polynomial effective criterion (P)_M, for M large enough. We furthermore give ellipticity criteria under which a random walk satisfying the polynomial effective criterion, is ballistic, satisfies the annealed central limit theorem or the quenched central limit theorem.

math.PR↗

arXiv2012

Level 1 quenched large deviation principle for random walk in dynamic random environment

Consider a random walk in a time-dependent random environment on the lattice Zd. Recently, Rassoul-Agha, Seppalainen and Yilmaz [RSY11] proved a general large deviation principle under mild ergodicity assumptions on the random environment for such a random walk, establishing first level 2 and 3 large deviation principles. Here we present two alternative short proofs of the level 1 large deviations under mild ergodicity assumptions on the environment: one for the continuous time case and another one for the discrete time case. Both proofs provide the existence, continuity and convexity of the rate function. Our methods are based on the use of the sub-additive ergodic theorem as presented by Varadhan in 2003.

math.PR↗