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The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes' input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
To operate effectively in the real world, agents should be able to act from high-dimensional raw sensory input such as images and achieve diverse goals across long time-horizons. Current deep reinforcement and imitation learning methods can…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
The importance of aggregated count data, which is calculated from the data of multiple individuals, continues to increase. Collective Graphical Model (CGM) is a probabilistic approach to the analysis of aggregated data. One of the most…
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…
In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several…
Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…
We consider continuous relational structures with finite domain $[n] := \{1, \ldots, n\}$ and a many valued logic, $CLA$, with values in the unit interval and which uses continuous connectives and continuous aggregation functions. $CLA$…
Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike…
This paper presents a novel solution paradigm of general optimization under both exogenous and endogenous uncertainties. This solution paradigm consists of a probability distribution (PD)-free method of obtaining deterministic equivalents…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
The preferential attachment (PA) model is a popular way of modeling dynamic social networks, such as collaboration networks. Assuming that the PA function takes a parametric form, we propose and study the maximum likelihood estimator of the…
We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…
We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…
The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in…
Probabilistic graphical models (PGMs) serve as a powerful framework for modeling complex systems with uncertainty and extracting valuable insights from data. However, users face challenges when applying PGMs to their problems in terms of…
In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear…