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Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…
Modus ponens (\emph{from $A$ and "if $A$ then $C$" infer $C$}, short: MP) is one of the most basic inference rules. The probabilistic MP allows for managing uncertainty by transmitting assigned uncertainties from the premises to the…
We introduce a framework to describe probabilistic models in Bell experiments, and more generally in contextuality scenarios. Such a scenario is a hypergraph whose vertices represent elementary events and hyperedges correspond to…
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…
We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate…
In recent years, model collapse has become a critical issue in language model training, making it essential to understand the underlying mechanisms driving this phenomenon. In this paper, we investigate recursive parametric model training…
There are two prominent paradigms to the modeling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
The Markov Decision Process (MDP) is a popular framework for sequential decision-making problems, and uncertainty quantification is an essential component of it to learn optimal decision-making strategies. In particular, a Bayesian…
Probabilistic models are a critical part of the modern deep learning toolbox - ranging from generative models (VAEs, GANs), sequence to sequence models used in machine translation and speech processing to models over functional spaces…
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…
Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes' rule to find the best explanation for available data. Understanding the neural mechanisms underlying…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
Recent works have proposed various explanations for the ability of modern large language models (LLMs) to perform in-context prediction. We propose an alternative conceptual viewpoint from an information-geometric and statistical…
A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of…
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…