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In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as…

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…

Let $T$ be a regular rooted tree. For every natural number $n$, let $B_n$ be the finite subtree of vertices with graph distance at most $n$ from the root. Consider the following forest-fire model on $B_n$: Each vertex can be "vacant" or…

State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…

In this chapter of the e-book "Self-Organized Criticality Systems" we summarize some theoretical approaches to self-organized criticality (SOC) phenomena that involve percolation as an essential key ingredient. Scaling arguments, random…

Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response…

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…

We introduce an exact distributed algorithm to train Random Forest models as well as other decision forest models without relying on approximating best split search. We explain the proposed algorithm and compare it to related approaches for…

A new family of tree models is proposed, which we call "differential trees." A differential tree model is constructed from multiple data sets and aims to detect distributional differences between them. The new methodology differs from the…

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…

The idle computers on a local area, campus area, or even wide area network represent a significant computational resource---one that is, however, also unreliable, heterogeneous, and opportunistic. This type of resource has been used…

Coordinate ascent variational inference is an important algorithm for inference in probabilistic models, but it is slow because it updates only a single variable at a time. Block coordinate methods perform inference faster by updating…

Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…

Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to…

Predicting future states in uncertain environments, such as wildfire spread, medical diagnosis, or autonomous driving, requires models that can consider multiple plausible outcomes. While diffusion models can effectively learn such…

Achieving energy-efficient trajectory planning for autonomous driving remains a challenge due to the limitations of model-agnostic approaches. This study addresses this gap by introducing an online nonlinear programming trajectory…

Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting.…

In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic…

In recent years, increased wildfires have caused irreversible damage to forest resources worldwide, threatening wildlives and human living conditions. The lack of accurate frontline information in real-time can pose great risks to…

Recently, fitting probabilistic models have gained importance in many areas but estimation of such distributional models with very large data sets is a difficult task. In particular, the use of rather complex models can easily lead to…