A long memory and non-linear realized volatility model class is proposed for direct Value at Risk (VaR) forecasting. This model, referred to as RNN-HAR, extends the heterogeneous autoregressive (HAR) model, a framework known for efficiently capturing long memory in realized measures, by integrating a Recurrent Neural Network (RNN) to handle non-linear dynamics. Loss-based generalized Bayesian inference with Sequential Monte Carlo is employed for model estimation and sequential prediction in RNN HAR. The empirical analysis is conducted using daily closing prices and realized measures from 2000 to 2022 across 31 market indices. The proposed models one step ahead VaR forecasting performance is compared against a basic HAR model and its extensions. The results demonstrate that the proposed RNN-HAR model consistently outperforms all other models considered in the study.

Evaluating different training interventions to determine which produce the best learning outcomes is one of the main challenges faced by instructional designers. Typically, these designers use A/B experiments to evaluate each intervention; however, it is costly and time consuming to run such studies. To address this issue, we explore how computational models of learning might support designers in reasoning causally about alternative interventions within a fractions tutor. We present an approach for automatically tuning models to specific individuals and show that personalized models make better predictions of students' behavior than generic ones. Next, we conduct simulations to generate counterfactual predictions of performance and learning for two students (high and low performing) in different versions of the fractions tutor. Our approach makes predictions that align with previous human findings, as well as testable predictions that might be evaluated with future human experiments.

Categorization of business processes is an important part of auditing. Large amounts of transactional data in auditing can be represented as transactions between financial accounts using weighted bipartite graphs. We view such bipartite graphs as many-valued formal contexts, which we use to obtain explainable categorization of these business processes in terms of financial accounts involved in a business process by using methods in formal concept analysis. We use Dempster-Shafer mass functions to represent agendas showing different interest in different set of financial accounts. We also model some possible deliberation scenarios between agents with different interrogative agendas to reach an aggregated agenda and categorization. The framework developed in this paper provides a formal ground to obtain and study explainable categorizations from the data represented as bipartite graphs according to the agendas of different agents in an organization (e.g. an audit firm), and interaction between these through deliberation. We use this framework to describe a machine-leaning meta algorithm for outlier detection and classification which can provide local and global explanations of its result and demonstrate it through an outlier detection algorithm.

The application of autonomous robotics to close-contact healthcare tasks has a clear role for the future due to its potential to reduce infection risks to staff and improve clinical efficiency. Nasopharyngeal (NP) swab sample collection for diagnosing upper-respiratory illnesses is one type of close contact task that is interesting for robotics due to the dexterity requirements and the unobservability of the nasal cavity. We propose a control system that performs the test using a collaborative manipulator arm with an instrumented end-effector to take visual and force measurements, under the scenario that the patient is unrestrained and the tools are general enough to be applied to other close contact tasks. The system employs a visual servo controller to align the swab with the nostrils. A compliant joint velocity controller inserts the swab along a trajectory optimized through a simulation environment, that also reacts to measured forces applied to the swab. Additional subsystems include a fuzzy logic system for detecting when the swab reaches the nasopharynx and a method for detaching the swab and aborting the procedure if safety criteria is violated. The system is evaluated using a second robotic arm that holds a nasal cavity phantom and simulates the natural head motions that could occur during the procedure. Through extensive experiments, we identify controller configurations capable of effectively performing the NP swab test even with significant head motion, which demonstrates the safety and reliability of the system.

Gibbs sampling is one of the most commonly used Markov Chain Monte Carlo (MCMC) algorithms due to its simplicity and efficiency. It cycles through the latent variables, sampling each one from its distribution conditional on the current values of all the other variables. Conventional Gibbs sampling is based on the systematic scan (with a deterministic order of variables). In contrast, in recent years, Gibbs sampling with random scan has shown its advantage in some scenarios. However, almost all the analyses of Gibbs sampling with the random scan are based on uniform selection of variables. In this paper, we focus on a random scan Gibbs sampling method that selects each latent variable non-uniformly. Firstly, we show that this non-uniform scan Gibbs sampling leaves the target posterior distribution invariant. Then we explore how to determine the selection probability for latent variables. In particular, we construct an objective as a function of the selection probability and solve the constrained optimization problem. We further derive an analytic solution of the selection probability, which can be estimated easily. Our algorithm relies on the simple intuition that choosing the variable updates according to their marginal probabilities enhances the mixing time of the Markov chain. Finally, we validate the effectiveness of the proposed Gibbs sampler by conducting a set of experiments on real-world applications.

Obtaining accurate inference and faithful uncertainty quantification in reasonable time is a frontier of today's statistical research (Cranmer et al., 2020). One major difficulty arising in most experimental and almost all observational data is the presence of complex dependency structures, for example, due to natural groupings (e.g., data gathered in different countries) or repeated measurements of the same observational units over time (e.g., particles, bacteria, or people; Gelman and Hill, 2006). To leverage these dependency structures, multilevel models (MLMs), also referred to as latent variable, hierarchical, random, or mixed effects models, have become an integral part of modern Bayesian statistics (Goldstein, 2011; Gelman et al., 2013; McGlothlin and Viele, 2018; Finch et al., 2019; Yao et al., 2022). Despite the wide success of Bayesian MLMs across the quantitative sciences, a major challenge is their limited efficiency and scalability when dealing with large and complex data. This is because estimating the full posterior distribution of all parameters of interest can be very costly (Gelman et al., 2013).

Is there a way to design powerful AI systems based on machine learning methods that would satisfy probabilistic safety guarantees? With the long-term goal of obtaining a probabilistic guarantee that would apply in every context, we consider estimating a context-dependent bound on the probability of violating a given safety specification. Such a risk evaluation would need to be performed at run-time to provide a guardrail against dangerous actions of an AI. Noting that different plausible hypotheses about the world could produce very different outcomes, and because we do not know which one is right, we derive bounds on the safety violation probability predicted under the true but unknown hypothesis. Such bounds could be used to reject potentially dangerous actions. Our main results involve searching for cautious but plausible hypotheses, obtained by a maximization that involves Bayesian posteriors over hypotheses. We consider two forms of this result, in the iid case and in the non-iid case, and conclude with open problems towards turning such theoretical results into practical AI guardrails.

Offline reinforcement learning (RL) learns policies from a fixed dataset, but often requires large amounts of data. The challenge arises when labeled datasets are expensive, especially when rewards have to be provided by human labelers for large datasets. In contrast, unlabelled data tends to be less expensive. This situation highlights the importance of finding effective ways to use unlabelled data in offline RL, especially when labelled data is limited or expensive to obtain. In this paper, we present the algorithm to utilize the unlabeled data in the offline RL method with kernel function approximation and give the theoretical guarantee. We present various eigenvalue decay conditions of $\mathcal{H}_k$ which determine the complexity of the algorithm. In summary, our work provides a promising approach for exploiting the advantages offered by unlabeled data in offline RL, whilst maintaining theoretical assurances.

We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. We sharpen prior work, proving that accurate recovery in the Wasserstein distance is possible with more noise than previously known. As a main application, our result yields a simple "linear query" algorithm for constructing a differentially private synthetic data distribution with Wasserstein-1 error $\tilde{O}(1/n)$ based on a dataset of $n$ points in $[-1,1]$. This bound is optimal up to log factors and matches a recent breakthrough of Boedihardjo, Strohmer, and Vershynin [Probab. Theory. Rel., 2024], which uses a more complex "superregular random walk" method to beat an $O(1/\sqrt{n})$ accuracy barrier inherent to earlier approaches. We illustrate a second application of our new moment-based recovery bound in numerical linear algebra: by improving an approach of Braverman, Krishnan, and Musco [STOC 2022], our result yields a faster algorithm for estimating the spectral density of a symmetric matrix up to small error in the Wasserstein distance.

Control affine assumptions, human inputs are external disturbances, in certified safe controller synthesis approaches are frequently violated in operational deployment under causal human actions. This paper takes a human-in-the-loop human-in-the-plant (HIL-HIP) approach towards ensuring operational safety of safety critical autonomous systems: human and real world controller (RWC) are modeled as a unified system. A three-way interaction is considered: a) through personalized inputs and biological feedback processes between HIP and HIL, b) through sensors and actuators between RWC and HIP, and c) through personalized configuration changes and data feedback between HIL and RWC. We extend control Lyapunov theory by generating barrier function (CLBF) under human action plans, model the HIL as a combination of Markov Chain for spontaneous events and Fuzzy inference system for event responses, the RWC as a black box, and integrate the HIL-HIP model with neural architectures that can learn CLBF certificates. We show that synthesized HIL-HIP controller for automated insulin delivery in Type 1 Diabetes is the only controller to meet safety requirements for human action inputs.