Sequential Monte Carlo Squared (SMC$^2$) is a Bayesian method which can infer the states and parameters of non-linear, non-Gaussian state-space models. The standard random-walk proposal in SMC$^2$ faces challenges, particularly with high-dimensional parameter spaces. This study outlines a novel approach by harnessing first-order gradients derived from a Common Random Numbers - Particle Filter (CRN-PF) using PyTorch. The resulting gradients can be leveraged within a Langevin proposal without accept/reject. Including Langevin dynamics within the proposal can result in a higher effective sample size and more accurate parameter estimates when compared with the random-walk. The resulting algorithm is parallelized on distributed memory using Message Passing Interface (MPI) and runs in $\mathcal{O}(\log_2N)$ time complexity. Utilizing 64 computational cores we obtain a 51x speed-up when compared to a single core. A GitHub link is given which provides access to the code.

Humans and many animals show remarkably adaptive behavior and can respond differently to the same input depending on their internal goals. The brain not only represents the intermediate abstractions needed to perform a computation but also actively maintains a representation of the computation itself (task abstraction). Such separation of the computation and its abstraction is associated with faster learning, flexible decision-making, and broad generalization capacity. We investigate if such benefits might extend to neural networks trained with task abstractions. For such benefits to emerge, one needs a task inference mechanism that possesses two crucial abilities: First, the ability to infer abstract task representations when no longer explicitly provided (task inference), and second, manipulate task representations to adapt to novel problems (task recomposition). To tackle this, we cast task inference as an optimization problem from a variational inference perspective and ground our approach in an expectation-maximization framework. We show that gradients backpropagated through a neural network to a task representation layer are an efficient heuristic to infer current task demands, a process we refer to as gradient-based inference (GBI). Further iterative optimization of the task representation layer allows for recomposing abstractions to adapt to novel situations. Using a toy example, a novel image classifier, and a language model, we demonstrate that GBI provides higher learning efficiency and generalization to novel tasks and limits forgetting. Moreover, we show that GBI has unique advantages such as preserving information for uncertainty estimation and detecting out-of-distribution samples.

We propose a globally optimal Bayesian network structure discovery algorithm based on a progressively leveled scoring approach. Bayesian network structure discovery is a fundamental yet NP-hard problem in the field of probabilistic graphical models, and as the number of variables increases, memory usage grows exponentially. The simple and effective method proposed by Silander and Myllym\"aki has been widely applied in this field, as it incrementally calculates local scores to achieve global optimality. However, existing methods that utilize disk storage, while capable of handling networks with a larger number of variables, introduce issues such as latency, fragmentation, and additional overhead associated with disk I/O operations. To avoid these problems, we explore how to further enhance computational efficiency and reduce peak memory usage using only memory. We introduce an efficient hierarchical computation method that requires only a single traversal of all local structures, retaining only the data and information necessary for the current computation, thereby improving efficiency and significantly reducing memory requirements. Experimental results indicate that our method, when using only memory, not only reduces peak memory usage but also improves computational efficiency compared to existing methods, demonstrating good scalability for handling larger networks and exhibiting stable experimental results. Ultimately, we successfully achieved the processing of a Bayesian network with 28 variables using only memory.

Recent studies seek to provide Graph Neural Network (GNN) interpretability via multiple unsupervised learning models. Due to the scarcity of datasets, current methods easily suffer from learning bias. To solve this problem, we embed a Large Language Model (LLM) as knowledge into the GNN explanation network to avoid the learning bias problem. We inject LLM as a Bayesian Inference (BI) module to mitigate learning bias. The efficacy of the BI module has been proven both theoretically and experimentally. We conduct experiments on both synthetic and real-world datasets. The innovation of our work lies in two parts: 1. We provide a novel view of the possibility of an LLM functioning as a Bayesian inference to improve the performance of existing algorithms; 2. We are the first to discuss the learning bias issues in the GNN explanation problem.

Colorectal polyps are generally benign alterations that, if not identified promptly and managed successfully, can progress to cancer and cause affectations on the colon mucosa, known as adenocarcinoma. Today advances in Deep Learning have demonstrated the ability to achieve significant performance in image classification and detection in medical diagnosis applications. Nevertheless, these models are prone to overfitting, and making decisions based only on point estimations may provide incorrect predictions. Thus, to obtain a more informed decision, we must consider point estimations along with their reliable uncertainty quantification. In this paper, we built different Bayesian neural network approaches based on the flexibility of posterior distribution to develop semantic segmentation of colorectal polyp images. We found that these models not only provide state-of-the-art performance on the segmentation of this medical dataset but also, yield accurate uncertainty estimates. We applied multiplicative normalized flows(MNF) and reparameterization trick on the UNET, FPN, and LINKNET architectures tested with multiple backbones in deterministic and Bayesian versions. We report that the FPN + EfficientnetB7 architecture with MNF is the most promising option given its IOU of 0.94 and Expected Calibration Error (ECE) of 0.004, combined with its superiority in identifying difficult-to-detect colorectal polyps, which is effective in clinical areas where early detection prevents the development of colon cancer.

The space of human goals is tremendously vast; and yet, from just a few moments of watching a scene or reading a story, we seem to spontaneously infer a range of plausible motivations for the people and characters involved. What explains this remarkable capacity for intuiting other agents' goals, despite the infinitude of ends they might pursue? And how does this cohere with our understanding of other people as approximately rational agents? In this paper, we introduce a sequential Monte Carlo model of open-ended goal inference, which combines top-down Bayesian inverse planning with bottom-up sampling based on the statistics of co-occurring subgoals. By proposing goal hypotheses related to the subgoals achieved by an agent, our model rapidly generates plausible goals without exhaustive search, then filters out goals that would be irrational given the actions taken so far. We validate this model in a goal inference task called Block Words, where participants try to guess the word that someone is stacking out of lettered blocks. In comparison to both heuristic bottom-up guessing and exact Bayesian inference over hundreds of goals, our model better predicts the mean, variance, efficiency, and resource rationality of human goal inferences, achieving similar accuracy to the exact model at a fraction of the cognitive cost, while also explaining garden-path effects that arise from misleading bottom-up cues. Our experiments thus highlight the importance of uniting top-down and bottom-up models for explaining the speed, accuracy, and generality of human theory-of-mind.

Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding transitions in financial, economic, social, environmental, and technological contexts. Building upon the Bayesian approach introduced in \cite{c:07}, we devise a new method for online change point detection in the mean of a univariate time series, which is well suited for real-time applications and is able to handle the general temporal patterns displayed by data in many empirical contexts. We first describe time series as an autoregressive process of an arbitrary order. Second, the variance and correlation of the data are allowed to vary within each regime driven by a scoring rule that updates the value of the parameters for a better fit of the observations. Finally, a change point is detected in a probabilistic framework via the posterior distribution of the current regime length. By modeling temporal dependencies and time-varying parameters, the proposed approach enhances both the estimate accuracy and the forecasting power. Empirical validations using various datasets demonstrate the method's effectiveness in capturing memory and dynamic patterns, offering deeper insights into the non-stationary dynamics of real-world systems.

We introduce neural information field filter, a Bayesian state and parameter estimation method for high-dimensional nonlinear dynamical systems given large measurement datasets. Solving such a problem using traditional methods, such as Kalman and particle filters, is computationally expensive. Information field theory is a Bayesian approach that can efficiently reconstruct dynamical model state paths and calibrate model parameters from noisy measurement data. To apply the method, we parameterize the time evolution state path using the span of a finite linear basis. The existing method has to reparameterize the state path by initial states to satisfy the initial condition. Designing an expressive yet simple linear basis before knowing the true state path is crucial for inference accuracy but challenging. Moreover, reparameterizing the state path using the initial state is easy to perform for a linear basis, but is nontrivial for more complex and expressive function parameterizations, such as neural networks. The objective of this paper is to simplify and enrich the class of state path parameterizations using neural networks for the information field theory approach. To this end, we propose a generalized physics-informed conditional prior using an auxiliary initial state. We show the existing reparameterization is a special case. We parameterize the state path using a residual neural network that consists of a linear basis function and a Fourier encoding fully connected neural network residual function. The residual function aims to correct the error of the linear basis function. To sample from the intractable posterior distribution, we develop an optimization algorithm, nested stochastic variational inference, and a sampling algorithm, nested preconditioned stochastic gradient Langevin dynamics. A series of numerical and experimental examples verify and validate the proposed method.

This is the author's version of the article that has been published in IEEE Transactions on Visualization and Computer Graphics. The final version of this record is available at: xx.xxxx/TVCG.201x.xxxxxxx/ Abstract--People commonly utilize visualizations not only to examine a given dataset, but also to draw generalizable conclusions about the underlying models or phenomena. Prior research has compared human visual inference to that of an optimal Bayesian agent, with deviations from rational analysis viewed as problematic. However, human reliance on non-normative heuristics may prove advantageous in certain circumstances. We investigate scenarios where human intuition might surpass idealized statistical rationality. In two experiments, we examine individuals' accuracy in characterizing the parameters of known data-generating models from bivariate visualizations. Our findings indicate that, although participants generally exhibited lower accuracy compared to statistical models, they frequently outperformed Bayesian agents, particularly when faced with extreme samples. Participants appeared to rely on their internal models to filter out noisy visualizations, thus improving their resilience against spurious data. However, participants displayed overconfidence and struggled with uncertainty estimation. They also exhibited higher variance than statistical machines. Our findings suggest that analyst gut reactions to visualizations may provide an advantage, even when departing from rationality. These results carry implications for designing visual analytics tools, offering new perspectives on how to integrate statistical models and analyst intuition for improved inference and decision-making. The data and materials for this paper are available at https://osf.io/qmfv6

Camera pose estimation is a fundamental problem in robotics. This paper focuses on two issues of interest: First, point and line features have complementary advantages, and it is of great value to design a uniform algorithm that can fuse them effectively; Second, with the development of modern front-end techniques, a large number of features can exist in a single image, which presents a potential for highly accurate robot pose estimation. With these observations, we propose AOPnP(L), an optimal linear-time camera-robot pose estimation algorithm from points and lines. Specifically, we represent a line with two distinct points on it and unify the noise model for point and line measurements where noises are added to 2D points in the image. By utilizing Plucker coordinates for line parameterization, we formulate a maximum likelihood (ML) problem for combined point and line measurements. To optimally solve the ML problem, AOPnP(L) adopts a two-step estimation scheme. In the first step, a consistent estimate that can converge to the true pose is devised by virtue of bias elimination. In the second step, a single Gauss-Newton iteration is executed to refine the initial estimate. AOPnP(L) features theoretical optimality in the sense that its mean squared error converges to the Cramer-Rao lower bound. Moreover, it owns a linear time complexity. These properties make it well-suited for precision-demanding and real-time robot pose estimation. Extensive experiments are conducted to validate our theoretical developments and demonstrate the superiority of AOPnP(L) in both static localization and dynamic odometry systems.