A Markov logic network (MLN) determines a probability distribution on the set of structures, or ``possible worlds'', with an arbitrary finite domain. We study the properties of such distributions as the domain size tends to infinity. Three types of concrete examples of MLNs will be considered, and the properties of random structures with domain sizes tending to infinity will be studied: (1) Arbitrary quantifier-free MLNs over a language with only one relation symbol which has arity 1. In this case we give a pretty complete characterization of the possible limit behaviours of random structures. (2) An MLN that favours graphs with fewer triangles (or more generally, fewer k-cliques). As a corollary of the analysis a ``$δ$-approximate 0-1 law'' for first-order logic is obtained. (3) An MLN that favours graphs with fewer vertices with degree higher than a fixed (but arbitrary) number. The analysis shows that depending on which ``soft constraints'' an MLN uses the limit behaviour of random structures can be quite different, and the weights of the soft constraints may, or may not, have influence on the limit behaviour. It will also be demonstrated, using (1), that quantifier-free MLNs and lifted Bayesian networks (in a broad sense) are asymptotically incomparable, roughly meaning that there is a sequence of distributions on possible worlds with increasing domain sizes that can be defined by one of the formalisms but not even approximated by the other. In a rather general context it is also shown that on large domains the distribution determined by an MLN concentrates almost all its probability mass on a totally different part of the space of possible worlds than the uniform distribution does.

Partial Optimal Transport (POT) has recently emerged as a central tool in various Machine Learning (ML) applications. It lifts the stringent assumption of the conventional Optimal Transport (OT) that input measures are of equal masses, which is often not guaranteed in real-world datasets, and thus offers greater flexibility by permitting transport between unbalanced input measures. Nevertheless, existing major solvers for POT commonly rely on entropic regularization for acceleration and thus return dense transport plans, hindering the adoption of POT in various applications that favor sparsity. In this paper, as an alternative approach to the entropic POT formulation in the literature, we propose a novel formulation of POT with quadratic regularization, hence termed quadratic regularized POT (QPOT), which induces sparsity to the transport plan and consequently facilitates the adoption of POT in many applications with sparsity requirements. Extensive experiments on synthetic and CIFAR-10 datasets, as well as real-world applications such as color transfer and domain adaptations, consistently demonstrate the improved sparsity and favorable performance of our proposed QPOT formulation.

The U.S. military will deploy several long-range surveillance drones to Okinawa Prefecture, near Japan's far-flung southwestern islands area near Taiwan, as the allies seek to counter China's ramped-up drone presence in the same area. Defense Minister Gen Nakatani said Tuesday that the U.S. MQ-4C Triton drones will be sent to the U.S. air base in Kadena, on Okinawa's main island, in the coming weeks. "This deployment is expected to enhance the Japan-U.S. alliance's intelligence-gathering capabilities and, by extension, the alliance's deterrence and response capabilities," Nakatani told a news conference.

--In this work, we investigate causal learning of independent causal mechanisms from a Bayesian perspective. Confirming previous claims from the literature, we show in a didactically accessible manner that unlabeled data (i.e., cause realizations) do not improve the estimation of the parameters defining the mechanism. Furthermore, we observe the importance of choosing an appropriate prior for the cause and mechanism parameters, respectively. Specifically, we show that a factorized prior results in a factorized posterior, which resonates with Janz-ing and Sch olkopf's definition of independent causal mechanisms via the Kolmogorov complexity of the involved distributions and with the concept of parameter independence of Heckerman et al. Impact Statement --Learning the effect from a given cause is an important problem in many engineering disciplines, specifically in the field of surrogate modeling, which aims to reduce the computational cost of numerical simulations. Causal learning, however, cannot make use of unlabeled data - i.e., cause realizations - if the mechanism that produces the effect is independent from the cause. In this work, we recover this well-known fact from a Bayesian perspective.

As probabilistic models continue to permeate various facets of our society and contribute to scientific advancements, it becomes a necessity to go beyond traditional metrics such as predictive accuracy and error rates and assess their trustworthiness. Grounded in the competence-based theory of trust, this work formalizes I-trustworthy framework -- a novel framework for assessing the trustworthiness of probabilistic classifiers for inference tasks by linking local calibration to trustworthiness. To assess I-trustworthiness, we use the local calibration error (LCE) and develop a method of hypothesis-testing. This method utilizes a kernel-based test statistic, Kernel Local Calibration Error (KLCE), to test local calibration of a probabilistic classifier. This study provides theoretical guarantees by offering convergence bounds for an unbiased estimator of KLCE. Additionally, we present a diagnostic tool designed to identify and measure biases in cases of miscalibration. The effectiveness of the proposed test statistic is demonstrated through its application to both simulated and real-world datasets. Finally, LCE of related recalibration methods is studied, and we provide evidence of insufficiency of existing methods to achieve I-trustworthiness.

Consider the communication-constrained estimation of discrete distributions under $\ell^p$ losses, where each distributed terminal holds multiple independent samples and uses limited number of bits to describe the samples. We obtain the minimax optimal rates of the problem in most parameter regimes. An elbow effect of the optimal rates at $p=2$ is clearly identified. To show the optimal rates, we first design estimation protocols to achieve them. The key ingredient of these protocols is to introduce adaptive refinement mechanisms, which first generate rough estimate by partial information and then establish refined estimate in subsequent steps guided by the rough estimate. The protocols leverage successive refinement, sample compression, thresholding and random hashing methods to achieve the optimal rates in different parameter regimes. The optimality of the protocols is shown by deriving compatible minimax lower bounds.

The city government of Ishigaki, Okinawa Prefecture, has conducted its third marine survey around the Japanese-administered Senkaku Islands, with Jiji Press and other reporters allowed to board its survey ship. During the survey, which lasted from Thursday to Saturday, Chinese coast guard vessels entered Japanese waters around the islands and attempted to interfere with the city's ship, but Japan Coast Guard vessels blocked the move. The city survey ship's journey to the area was the first since January last year. The latest survey was joined by Ishigaki Mayor Yoshitaka Nakayama and some lawmakers, including former Defense Minister Tomomi Inada. The Japanese government did not allow the survey participants to land on the islands.

In a factory run by Nakamatsu Meat, a small "meat shop in town" with a 42-year history in Uruma, Okinawa Prefecture, a part-time employee speaks into a small monitor: "Alexa, I made five cases of ham and cheese sandwiches." Alexa, an artificial-intelligence powered voice assistant from Amazon, then turns the report into data that is compiled in the firm's computer. "At first, workers were a little shy about talking to a machine," said Kazumi Nakamoto, the company's executive director. "But now they are used to it, and they even say'Alexa, good morning.'"

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian state-space models in complex environments. Existing differentiable particle filters are mostly constructed with vanilla neural networks that do not allow density estimation. As a result, they are either restricted to a bootstrap particle filtering framework or employ predefined distribution families (e.g. Gaussian distributions), limiting their performance in more complex real-world scenarios. In this paper we present a differentiable particle filtering framework that uses (conditional) normalising flows to build its dynamic model, proposal distribution, and measurement model. This not only enables valid probability densities but also allows the proposed method to adaptively learn these modules in a flexible way, without being restricted to predefined distribution families. We derive the theoretical properties of the proposed filters and evaluate the proposed normalising flow-based differentiable particle filters' performance through a series of numerical experiments.

This paper addresses intervention-based causal representation learning (CRL) under a general nonparametric latent causal model and an unknown transformation that maps the latent variables to the observed variables. Linear and general transformations are investigated. The paper addresses both the \emph{identifiability} and \emph{achievability} aspects. Identifiability refers to determining algorithm-agnostic conditions that ensure recovering the true latent causal variables and the latent causal graph underlying them. Achievability refers to the algorithmic aspects and addresses designing algorithms that achieve identifiability guarantees. By drawing novel connections between \emph{score functions} (i.e., the gradients of the logarithm of density functions) and CRL, this paper designs a \emph{score-based class of algorithms} that ensures both identifiability and achievability. First, the paper focuses on \emph{linear} transformations and shows that one stochastic hard intervention per node suffices to guarantee identifiability. It also provides partial identifiability guarantees for soft interventions, including identifiability up to ancestors for general causal models and perfect latent graph recovery for sufficiently non-linear causal models. Secondly, it focuses on \emph{general} transformations and shows that two stochastic hard interventions per node suffice for identifiability. Notably, one does \emph{not} need to know which pair of interventional environments have the same node intervened.