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Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or…

A key contributing factor to incredible success of deep neural networks has been the significant rise on massively parallel computing devices allowing researchers to greatly increase the size and depth of deep neural networks, leading to…

Inferring stochastic dynamics from data is central across the sciences, yet in many applications only unordered, non-sequential measurements are available-often restricted to limited regions of state space-so standard time-series methods do…

Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time…

This paper focuses on the Bayesian Network Propensity Score (BNPS), a novel approach for estimating treatment effects in observational studies characterized by unknown (and likely unbalanced) designs and complex dependency structures among…

Computer networks have become a critical infrastructure. In fact, networks should not only meet strict requirements in terms of correctness, availability, and performance, but they should also be very flexible and support fast updates,…

Probabilistic programming has become a standard practice to model stochastic events and learn about the behavior of nature in different scientific contexts, ranging from Genetics and Ecology to Linguistics and Psychology. However, domain…

The study of dynamical systems on networks, describing complex interactive processes, provides insight into how network structure affects global behaviour. Yet many methods for network dynamics fail to cope with large or partially-known…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…

Distributed stochastic gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. However, the…

Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…

With the rapid development of Internet and the sharp increase of network crime, network security has become very important and received a lot of attention. We model security issues as stochastic systems. This allows us to find weaknesses in…

We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…

Stochastic network calculus is an evolving theory which accounts for statistical multiplexing and uses an envelope approach for probabilistic delay and backlog analysis of networks. One of the key ideas of stochastic network calculus is the…

Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…

We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…