We propose a novel neural networks based approach to efficiently answer arbitrary Most Probable Explanation (MPE) queries--a well-known NP-hard task--in large probabilistic models such as Bayesian and Markov networks, probabilistic circuits, and neural auto-regressive models. By arbitrary MPE queries, we mean that there is no predefined partition of variables into evidence and non-evidence variables. The key idea is to distill all MPE queries over a given probabilistic model into a neural network and then use the latter for answering queries, eliminating the need for time-consuming inference algorithms that operate directly on the probabilistic model. We improve upon this idea by incorporating inference-time optimization with self-supervised loss to iteratively improve the solutions and employ a teacher-student framework that provides a better initial network, which in turn, helps reduce the number of inference-time optimization steps. The teacher network utilizes a self-supervised loss function optimized for getting the exact MPE solution, while the student network learns from the teacher's near-optimal outputs through supervised loss.

In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent Metropolis-Adjusted Langevin Diffusion algorithm by modelling the stochasticity of precondition matrix as a random matrix. An advantage compared to other proposal method is that it only requires the gradient of log-posterior. The proposed method provides fully adaptation mechanisms to tune proposal densities to exploits and adapts the geometry of local structures of statistical models. We clarify the benefits of the new proposal by modelling a Quantum Probability Density Functions of a free particle in a plane (energy Eigen-functions). The proposed model represents a remarkable improvement in terms of performance accuracy and computational time over standard MCMC method.

The objective of the paper is to price weather derivative contracts based on temperature and precipitation as underlying climate variables.

Many-body open quantum systems archical equations of motion (HEOM) [20-24], dissipaton (OQS) have gained wide attention and found applications equation of motion (DEOM) [25, 26], and pseudomode in various fields including physics, chemistry, materials theory [27-30]; and stochastic methods, including quantum science, and life sciences. These applications cover state diffusion (QSD) [31-35], stochastic equation various fields such as coherent energy transfer in biological of motion (SEOM) [36-39], hierarchy of stochastic pure photosystems [1-3], charge transfer in molecular states (HOPS) [40], and quantum Monte Carlo (QMC) aggregates [4, 5], electron transport in single molecular [41, 42]. However, the computational cost of these methods junctions [6, 7], multidimensional coherent spectroscopy grows rapidly as the complexity of OQS increases. of condensed phase materials [8, 9], correlated quantum Here, complexity refers to the size of the system, the matter for quantum information and computation strength of many-body correlations, and the level of non- [10, 11], and precise measurement and control of local Markovianity.

Both approaches enable sampling and density estimation of conditional probability distributions, which are core tasks in Bayesian inference. Our methods represent the target conditional distributions as transformations of a tractable reference distribution and, therefore, fall into the framework of measure transport. COT maps are a canonical choice within this framework, with desirable properties such as uniqueness and monotonicity. However, the associated COT problems are computationally challenging, even in moderate dimensions. To improve the scalability, our numerical algorithms leverage neural networks to parameterize COT maps. Our methods exploit the structure of the static and dynamic formulations of the COT problem. PCP-Map models conditional transport maps as the gradient of a partially input convex neural network (PICNN) and uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. COT-Flow models conditional transports via the flow of a regularized neural ODE; it is slower to train but offers faster sampling. We demonstrate their effectiveness and efficiency by comparing them with state-of-the-art approaches using benchmark datasets and Bayesian inverse problems.

We propose a graphical structure for structural equation models that is stable under marginalization under linearity and Gaussianity assumptions. We show that computing the maximum likelihood estimation of this model is equivalent to training a neural network. We implement a GPU-based algorithm that computes the maximum likelihood estimation of these models.

This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.

This paper shows how the prices of option contracts traded in finan(cid:173) cial markets can be tracked sequentially by means of the Extended Kalman Filter algorithm. I consider call and put option pairs with identical strike price and time of maturity as a two output nonlin(cid:173) ear system. The Black-Scholes approach popular in Finance liter(cid:173) ature and the Radial Basis Functions neural network are used in modelling the nonlinear system generating these observations. I show how both these systems may be identified recursively using the EKF algorithm. I present results of simulations on some FTSE 100 Index options data and discuss the implications of viewing the pricing problem in this sequential manner.

In recent years, neural networks of various configurations have been increasingly used to analyze data obtained with fluorescent and Cherenkov telescopes. In particular, a whole series of studies dedicated to the analysis of gamma-ray astronomy data with neural networks has been performed by the VERITAS [1], TAIGA [2, 3], and CTA [4, 5] collaborations. Typical tasks are the recognition of particular signal patterns in the data flow. In the simplest case, the problem can be reduced to classifying data into two groups: data samples that contain a signal of the desired type and all the rest. Since data obtained with the help of telescopes can naturally be considered as images or animations, one of the popular tools for classifying them are convolutional neural networks (CNNs), created primarily for image classification. CNNs have demonstrated the highest efficiency in this class of problems, see, for example, [6, 7].

With millions of images and video content posted daily, visual filters have become an essential feature of social media platforms, allowing users to enhance and customize their video content with various effects and adjustments. These filters have revolutionized the way we communicate and share experiences, providing us with the ability to create visually appealing and engaging content that captures our audience's attention. Moreover, with the rise of AI, these filters have become even more sophisticated, allowing us to manipulate video content in previously impossible ways with just some clicks. AI-powered video filters can automatically adjust lighting, color balance, and other elements of a video, allowing creators to achieve a professional-quality look without the need for extensive technical knowledge. Although very powerful, these filters are designed with pre-defined parameters, so they cannot generate consistent color styles for images with diverse appearances.