Predicting the S&P 500 index volatility is crucial for investors and financial analysts as it helps assess market risk and make informed investment decisions. Volatility represents the level of uncertainty or risk related to the size of changes in a security's value, making it an essential indicator for financial planning. This study explores four methods to improve the accuracy of volatility forecasts for the S&P 500: the established GARCH model, known for capturing historical volatility patterns; an LSTM network that utilizes past volatility and log returns; a hybrid LSTM-GARCH model that combines the strengths of both approaches; and an advanced version of the hybrid model that also factors in the VIX index to gauge market sentiment. This analysis is based on a daily dataset that includes S&P 500 and VIX index data, covering the period from January 3, 2000, to December 21, 2023. Through rigorous testing and comparison, we found that machine learning approaches, particularly the hybrid LSTM models, significantly outperform the traditional GARCH model. Including the VIX index in the hybrid model further enhances its forecasting ability by incorporating real-time market sentiment. The results of this study offer valuable insights for achieving more accurate volatility predictions, enabling better risk management and strategic investment decisions in the volatile environment of the S&P 500.

This study addresses the challenge of stroke diagnosis and treatment under uncertainty, a critical issue given the rapid progression and severe consequences of stroke conditions such as aneurysms, arteriovenous malformations (AVM), and occlusions. Current diagnostic methods, including Digital Subtraction Angiography (DSA), face limitations due to high costs and its invasive nature. To overcome these challenges, we propose a novel approach using a Partially Observable Markov Decision Process (POMDP) framework. Our model integrates advanced diagnostic tools and treatment approaches with a decision-making algorithm that accounts for the inherent uncertainties in stroke diagnosis. Our approach combines noisy observations from CT scans, Siriraj scores, and DSA reports to inform the subsequent treatment options. We utilize the online solver DESPOT, which employs tree-search methods and particle filters, to simulate potential future scenarios and guide our strategies. The results indicate that our POMDP framework balances diagnostic and treatment objectives, striking a tradeoff between the need for precise stroke identification via invasive procedures like DSA and the constraints of limited healthcare resources that necessitate more cost-effective strategies, such as in-hospital or at-home observation, by relying only relying on simulation rollouts and not imposing any prior knowledge. Our study offers a significant contribution by presenting a systematic framework that optimally integrates diagnostic and treatment processes for stroke and accounting for various uncertainties, thereby improving care and outcomes in stroke management.

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

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research - we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime.

Image segmentation relies heavily on neural networks which are known to be overconfident, especially when making predictions on out-of-distribution (OOD) images. This is a common scenario in the medical domain due to variations in equipment, acquisition sites, or image corruptions. This work addresses the challenge of OOD detection by proposing Laplacian Segmentation Networks (LSN): methods which jointly model epistemic (model) and aleatoric (data) uncertainty for OOD detection. In doing so, we propose the first Laplace approximation of the weight posterior that scales to large neural networks with skip connections that have high-dimensional outputs. We demonstrate on three datasets that the LSN-modeled parameter distributions, in combination with suitable uncertainty measures, gives superior OOD detection.

This paper presents a comprehensive theoretical investigation into the parameterized complexity of explanation problems in various machine learning (ML) models. Contrary to the prevalent black-box perception, our study focuses on models with transparent internal mechanisms. We address two principal types of explanation problems: abductive and contrastive, both in their local and global variants. Our analysis encompasses diverse ML models, including Decision Trees, Decision Sets, Decision Lists, Ordered Binary Decision Diagrams, Random Forests, and Boolean Circuits, and ensembles thereof, each offering unique explanatory challenges. This research fills a significant gap in explainable AI (XAI) by providing a foundational understanding of the complexities of generating explanations for these models. This work provides insights vital for further research in the domain of XAI, contributing to the broader discourse on the necessity of transparency and accountability in AI systems.

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.

Autoregressive language models are the currently dominant paradigm for text generation, but they have some fundamental limitations that cannot be remedied by scale-for example inherently sequential and unidirectional generation. While alternate classes of models have been explored, we have limited mathematical understanding of their fundamental power and limitations. In this paper we focus on Generative Masked Language Models (GMLMs), a non-autoregressive paradigm in which we train a model to fit conditional probabilities of the data distribution via masking, which are subsequently used as inputs to a Markov Chain to draw samples from the model, These models empirically strike a promising speed-quality trade-off as each step can be typically parallelized by decoding the entire sequence in parallel. We develop a mathematical framework for analyzing and improving such models which sheds light on questions of sample complexity and inference speed and quality. Empirically, we adapt the T5 model for iteratively-refined parallel decoding, achieving 2-3x speedup in machine translation with minimal sacrifice in quality compared with autoregressive models. We run careful ablation experiments to give recommendations on key design choices, and make fine-grained observations on the common error modes in connection with our theory. Our mathematical analyses and empirical observations characterize both potentials and limitations of this approach, and can be applied to future works on improving understanding and performance of GMLMs. Our codes are released at https://github.com/google-research/google-research/tree/master/padir

Formulating a real-world problem under the Reinforcement Learning framework involves non-trivial design choices, such as selecting a discount factor for the learning objective (discounted cumulative rewards), which articulates the planning horizon of the agent. This work investigates the impact of the discount factor on the biasvariance trade-off given structural parameters of the underlying Markov Decision Process. Our results support the idea that a shorter planning horizon might be beneficial, especially under partial observability.