Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this paper, we propose an ensemble-based version of AIS by combining it with population-based Monte Carlo methods to improve its efficiency. By keeping track of an ensemble instead of a single particle along some continuation path between the starting distribution and the target distribution, we take advantage of the interaction within the ensemble to encourage the exploration of undiscovered modes. Specifically, our main idea is to utilize either the snooker algorithm or the genetic algorithm used in Evolutionary Monte Carlo. We discuss how the proposed algorithm can be implemented and derive a partial differential equation governing the evolution of the ensemble under the continuous time and mean-field limit. We also test the efficiency of the proposed algorithm on various continuous and discrete distributions.

The HERMES (High Energy Rapid Modular Ensemble of Satellites) Pathfinder mission serves as an in-orbit demonstration of a constellation of nanosatellites whose primary scientific purpose is to discover intense high-energy transients, such as gamma-ray bursts, across a broad energy range (few keV to few MeV) with unparalleled temporal precision and exact localisation. By 2024, the first constellation of six nanosatellites is expected to be launched. To fully exploit satellite data and allow faint astronomical events to emerge, a precise estimation of satellite background count rates is required to determine whether the event is statistically valid or not. The dynamics of the background are related to the satellite's orbital information, which varies in the order of minutes, potentially hiding long transient events. This work introduces two main contributions I have brought ahead; first a novel background estimator is presented that could potentially be fitted to any type of X/Gamma-ray satellite space telescope, capable of capturing long-term dynamics and accurate enough to detect faint transients. This estimator is built using a Neural Network and tested on data from the Fermi Gamma-ray Space Telescope's Gamma Burst Monitor (GBM). As a second objective, it is employed a trigger algorithm, called FOCuS (Functional Online CUSUM), to extract events from the background using the background estimator. The resulting framework, DeepGRB, can identify astronomical events that are both present and absent from the Fermi-GBM catalog. The analysis of the discovered events reveals the strengths and weaknesses of the framework.

Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our survey, we systematically and comprehensively review on diffusion-based graph generative methods. We first make a review on three mainstream paradigms of diffusion methods, which are denoising diffusion probabilistic models, score-based genrative models, and stochastic differential equations. Then we further categorize and introduce the latest applications of diffusion models on graphs. In the end, we point out some limitations of current studies and future directions of future explorations. The summary of existing methods metioned in this survey is in https://github.com/zhejiangzhuque/Diffusion-based-Graph-Generative-Methods.

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

Deep learning has become the dominating approach for object detection. To achieve accurate fine-grained detection, one needs to employ a large enough model and a vast amount of data annotations. In this paper, we propose a commonsense knowledge inference module (CKIM) which leverages commonsense knowledge to assist a lightweight deep neural network base coarse-grained object detector to achieve accurate fine-grained detection. Specifically, we focus on a scenario where a single image contains objects of similar categories but varying sizes, and we establish a size-related commonsense knowledge inference module (CKIM) that maps the coarse-grained labels produced by the DL detector to size-related fine-grained labels. Considering that rule-based systems are one of the popular methods of knowledge representation and reasoning, our experiments explored two types of rule-based CKIMs, implemented using crisp-rule and fuzzy-rule approaches, respectively. Experimental results demonstrate that compared with baseline methods, our approach achieves accurate fine-grained detection with a reduced amount of annotated data and smaller model size. Our code is available at: https://github.com/ZJLAB-AMMI/CKIM.

Time series clustering is an essential machine learning task with applications in many disciplines. While the majority of the methods focus on time series taking values on the real line, very few works consider time series defined on the unit circle, although the latter objects frequently arise in many applications. In this paper, the problem of clustering circular time series is addressed. To this aim, a distance between circular series is introduced and used to construct a clustering procedure. The metric relies on a new measure of serial dependence considering circular arcs, thus taking advantage of the directional character inherent to the series range. Since the dynamics of the series may vary over the time, we adopt a fuzzy approach, which enables the procedure to locate each series into several clusters with different membership degrees. The resulting clustering algorithm is able to group series generated from similar stochastic processes, reaching accurate results with series coming from a broad variety of models. An extensive simulation study shows that the proposed method outperforms several alternative techniques, besides being computationally efficient. Two interesting applications involving time series of wind direction in Saudi Arabia highlight the potential of the proposed approach.

State-of-the-art methods for Bayesian inference in state-space models are (a) conditional sequential Monte Carlo (CSMC) algorithms; (b) sophisticated 'classical' MCMC algorithms like MALA, or mGRAD from Titsias and Papaspiliopoulos (2018, arXiv:1610.09641v3 [stat.ML]). The former propose $N$ particles at each time step to exploit the model's 'decorrelation-over-time' property and thus scale favourably with the time horizon, $T$ , but break down if the dimension of the latent states, $D$, is large. The latter leverage gradient-/prior-informed local proposals to scale favourably with $D$ but exhibit sub-optimal scalability with $T$ due to a lack of model-structure exploitation. We introduce methods which combine the strengths of both approaches. The first, Particle-MALA, spreads $N$ particles locally around the current state using gradient information, thus extending MALA to $T > 1$ time steps and $N > 1$ proposals. The second, Particle-mGRAD, additionally incorporates (conditionally) Gaussian prior dynamics into the proposal, thus extending the mGRAD algorithm to $T > 1$ time steps and $N > 1$ proposals. We prove that Particle-mGRAD interpolates between CSMC and Particle-MALA, resolving the 'tuning problem' of choosing between CSMC (superior for highly informative prior dynamics) and Particle-MALA (superior for weakly informative prior dynamics). We similarly extend other 'classical' MCMC approaches like auxiliary MALA, aGRAD, and preconditioned Crank-Nicolson-Langevin (PCNL) to $T > 1$ time steps and $N > 1$ proposals. In experiments, for both highly and weakly informative prior dynamics, our methods substantially improve upon both CSMC and sophisticated 'classical' MCMC approaches.

An adaptive control approach for a three-phase grid-interfaced solar photovoltaic system based on the new Neuro-Fuzzy Inference System with Rain Optimization Algorithm (ANROA) methodology is proposed and discussed in this manuscript. This method incorporates an Adaptive Neuro-fuzzy Inference System (ANFIS) with a Rain Optimization Algorithm (ROA). The ANFIS controller has excellent maximum tracking capability because it includes features of both neural and fuzzy techniques. The ROA technique is in charge of controlling the voltage source converter switching. Avoiding power quality problems including voltage fluctuations, harmonics, and flickers as well as unbalanced loads and reactive power usage is the major goal. Besides, the proposed method performs at zero voltage regulation and unity power factor modes. The suggested control approach has been modeled and simulated, and its performance has been assessed using existing alternative methods. A statistical analysis of proposed and existing techniques has been also presented and discussed. The results of the simulations demonstrate that, when compared to alternative approaches, the suggested strategy may properly and effectively identify the best global solutions. Furthermore, the system's robustness has been studied by using MATLAB/SIMULINK environment and experimentally by Field Programmable Gate Arrays Controller (FPGA)-based Hardware-in-Loop (HLL).

The feature selection in a traditional binary classification algorithm is always used in the stage of dataset preprocessing, which makes the obtained features not necessarily the best ones for the classification algorithm, thus affecting the classification performance. For a traditional rule-based binary classification algorithm, classification rules are usually deterministic, which results in the fuzzy information contained in the rules being ignored. To do so, this paper employs iterative feature selection in fuzzy rule-based binary classification. The proposed algorithm combines feature selection based on fuzzy correlation family with rule mining based on biclustering. It first conducts biclustering on the dataset after feature selection. Then it conducts feature selection again for the biclusters according to the feedback of biclusters evaluation. In this way, an iterative feature selection framework is build. During the iteration process, it stops until the obtained bicluster meets the requirements. In addition, the rule membership function is introduced to extract vectorized fuzzy rules from the bicluster and construct weak classifiers. The weak classifiers with good classification performance are selected by Adaptive Boosting and the strong classifier is constructed by "weighted average". Finally, we perform the proposed algorithm on different datasets and compare it with other peers. Experimental results show that it achieves good classification performance and outperforms its peers.

Several successful reinforcement learning algorithms make use of regularization to promote multi-modal policies that exhibit enhanced exploration and robustness. With functional approximation, the convergence properties of some of these algorithms (e.g. soft Q-learning) are not well understood. In this paper, we consider a single-loop algorithm for minimizing the projected Bellman error with finite time convergence guarantees in the case of linear function approximation. The algorithm operates on two scales: a slower scale for updating the target network of the state-action values, and a faster scale for approximating the Bellman backups in the subspace of the span of basis vectors. We show that, under certain assumptions, the proposed algorithm converges to a stationary point in the presence of Markovian noise. In addition, we provide a performance guarantee for the policies derived from the proposed algorithm.