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Popular artificial neural networks (ANN) optimize parameters for unidirectional value propagation, assuming some guessed parametrization type like Multi-Layer Perceptron (MLP) or Kolmogorov-Arnold Network (KAN). In contrast, for biological neurons e.g. "it is not uncommon for axonal propagation of action potentials to happen in both directions" \cite{axon} - suggesting they are optimized to continuously operate in multidirectional way. Additionally, statistical dependencies a single neuron could model is not just (expected) value dependence, but entire joint distributions including also higher moments. Such agnostic joint distribution neuron would allow for multidirectional propagation (of distributions or values) e.g. $\rho(x|y,z)$ or $\rho(y,z|x)$ by substituting to $\rho(x,y,z)$ and normalizing. There will be discussed Hierarchical Correlation Reconstruction (HCR) for such neuron model: assuming $\rho(x,y,z)=\sum_{ijk} a_{ijk} f_i(x) f_j(y) f_k(z)$ type parametrization of joint distribution with polynomial basis $f_i$, which allows for flexible, inexpensive processing including nonlinearities, direct model estimation and update, trained through standard backpropagation or novel ways for such structure up to tensor decomposition. Using only pairwise (input-output) dependencies, its expected value prediction becomes KAN-like with trained activation functions as polynomials, can be extended by adding higher order dependencies through included products - in conscious interpretable way, allowing for multidirectional propagation of both values and probability densities.

Community detection algorithms try to extract a mesoscale structure from the available network data, generally avoiding any explicit assumption regarding the quantity and quality of information conveyed by specific sets of edges. In this paper, we show that the core of ideological/discursive communities on X/Twitter can be effectively identified by uncovering the most informative interactions in an authors-audience bipartite network through a maximum-entropy null model. The analysis is performed considering three X/Twitter datasets related to the main political events of 2022 in Italy, using as benchmarks four state-of-the-art algorithms - three descriptive, one inferential -, and manually annotating nearly 300 verified users based on their political affiliation. In terms of information content, the communities obtained with the entropy-based algorithm are comparable to those obtained with some of the benchmarks. However, such a methodology on the authors-audience bipartite network: uses just a small sample of the available data to identify the central users of each community; returns a neater partition of the user set in just a few, easy to interpret, communities; clusters well-known political figures in a way that better matches the political alliances when compared with the benchmarks. Our results provide an important insight into online debates, highlighting that online interaction networks are mostly shaped by the activity of a small set of users who enjoy public visibility even outside social media.

This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a function, tapering off the effect of distant particles via local weighting. This introduces a candidate method (the locally weighted Ensemble Kalman method for inversion) with the motivation of combining some of the strengths of the particle filter (ability to cope with nonlinear maps and non-Gaussian distributions) and the Ensemble Kalman filter (no filter degeneracy).

Sequential DeepFake detection is an emerging task that aims to predict the manipulation sequence in order. Existing methods typically formulate it as an image-to-sequence problem, employing conventional Transformer architectures for detection. However, these methods lack dedicated design and consequently result in limited performance. In this paper, we propose a novel Texture-aware and Shape-guided Transformer to enhance detection performance. Our method features four major improvements. Firstly, we describe a texture-aware branch that effectively captures subtle manipulation traces with the Diversiform Pixel Difference Attention module. Then we introduce a Bidirectional Interaction Cross-attention module that seeks deep correlations among spatial and sequential features, enabling effective modeling of complex manipulation traces. To further enhance the cross-attention, we describe a Shape-guided Gaussian mapping strategy, providing initial priors of the manipulation shape. Finally, observing that the latter manipulation in a sequence may influence traces left in the earlier one, we intriguingly invert the prediction order from forward to backward, leading to notable gains as expected. Extensive experimental results demonstrate that our method outperforms others by a large margin, highlighting the superiority of our method.

We study the properties of a family of distances between functions of a single variable. These distances are examples of integral probability metrics, and have been used previously for comparing probability measures on the line; special cases include the Earth Mover's Distance and the Kolmogorov Metric. We examine their properties for general signals, proving that they are robust to a broad class of deformations. We also establish corresponding robustness results for the induced sliced distances between multivariate functions. Finally, we establish error bounds for approximating the univariate metrics from finite samples, and prove that these approximations are robust to additive Gaussian noise. The results are illustrated in numerical experiments, which include comparisons with Wasserstein distances.

The evaluation of text-generative vision-language models is a challenging yet crucial endeavor. By addressing the limitations of existing Visual Question Answering (VQA) benchmarks and proposing innovative evaluation methodologies, our research seeks to advance our understanding of these models' capabilities. We propose a novel VQA benchmark based on well-known visual classification datasets which allows a granular evaluation of text-generative vision-language models and their comparison with discriminative vision-language models. To improve the assessment of coarse answers on fine-grained classification tasks, we suggest using the semantic hierarchy of the label space to ask automatically generated follow-up questions about the ground-truth category. Finally, we compare traditional NLP and LLM-based metrics for the problem of evaluating model predictions given ground-truth answers. We perform a human evaluation study upon which we base our decision on the final metric. We apply our benchmark to a suite of vision-language models and show a detailed comparison of their abilities on object, action, and attribute classification. Our contributions aim to lay the foundation for more precise and meaningful assessments, facilitating targeted progress in the exciting field of vision-language modeling.

In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on frequency estimation using Schnieper's framework for claim numbering. We demonstrate that Schnieper's model is consistent with a Poisson distribution for the total number of claims above a priority at each year of development, providing a robust basis for parameter estimation. Additionally, we explain how to build an alternative assumption based on a Negative binomial distribution, which yields similar results. The study includes a bootstrap procedure to manage uncertainty in parameter estimation and a case study comparing assumptions and evaluating the impact of the bootstrap approach.

This thesis is a corpus-based, quantitative, and typological analysis of the functions of Early Slavic participle constructions and their finite competitors ($jegda$-'when'-clauses). The first part leverages detailed linguistic annotation on Early Slavic corpora at the morphosyntactic, dependency, information-structural, and lexical levels to obtain indirect evidence for different potential functions of participle clauses and their main finite competitor and understand the roles of compositionality and default discourse reasoning as explanations for the distribution of participle constructions and $jegda$-clauses in the corpus. The second part uses massively parallel data to analyze typological variation in how languages express the semantic space of English $when$, whose scope encompasses that of Early Slavic participle constructions and $jegda$-clauses. Probabilistic semantic maps are generated and statistical methods (including Kriging, Gaussian Mixture Modelling, precision and recall analysis) are used to induce cross-linguistically salient dimensions from the parallel corpus and to study conceptual variation within the semantic space of the hypothetical concept WHEN.

Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable model, such as a Hidden Markov model (HMM), these methods are designed to only estimate the parameters, rather than the joint distribution of the parameters and the hidden states. Naive application of these methods to a HMM, ignoring the inference of this joint posterior distribution, will thus produce an inaccurate estimate of the posterior predictive distribution, in turn hampering the assessment of goodness-of-fit. To rectify this problem, we propose a novel, sample-efficient likelihood-free method for estimating the high-dimensional hidden states of an implicit HMM. Our approach relies on learning directly the intractable posterior distribution of the hidden states, using an autoregressive-flow, by exploiting the Markov property. Upon evaluating our approach on some implicit HMMs, we found that the quality of the estimates retrieved using our method is comparable to what can be achieved using a much more computationally expensive SMC algorithm.

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to concentration in general metric spaces.