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In the real world, long sequence time-series forecasting (LSTF) is needed in many cases, such as power consumption prediction and air quality prediction.Multi-dimensional long time series model has more strict requirements on the model,…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
This paper introduces a new latent variable generative model able to handle high dimensional longitudinal data and relying on variational inference. The time dependency between the observations of an input sequence is modelled using…
Data-driven soft sensors help in process operations by providing real-time estimates of otherwise hard- to-measure process quantities, e.g., viscosities or product concentrations. Currently, soft sensors need to be developed individually…
Accurate electricity demand forecasting is essential for several reasons, especially as the integration of renewable energy sources and the transition to a decentralized network paradigm introduce greater complexity and uncertainty. The…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…
The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…
One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…
We present a purely deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long-range dependence. Parameters, such as the Hurst exponent, are critical in…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
Network data are often sampled with auxiliary information or collected through the observation of a complex system over time, leading to multiple network snapshots indexed by a continuous variable. Many methods in statistical network…
In many applications of finance, biology and sociology, complex systems involve entities interacting with each other. These processes have the peculiarity of evolving over time and of comprising latent factors, which influence the system…
Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains…