In this work, we study the low-rank MDPs with adversarially changed losses in the full-information feedback setting. In particular, the unknown transition probability kernel admits a low-rank matrix decomposition \citep{REPUCB22}, and the loss functions may change adversarially but are revealed to the learner at the end of each episode. We propose a policy optimization-based algorithm POLO, and we prove that it attains the $\widetilde{O}(K^{\frac{5}{6}}A^{\frac{1}{2}}d\ln(1+M)/(1-\gamma)^2)$ regret guarantee, where $d$ is rank of the transition kernel (and hence the dimension of the unknown representations), $A$ is the cardinality of the action space, $M$ is the cardinality of the model class, and $\gamma$ is the discounted factor. Notably, our algorithm is oracle-efficient and has a regret guarantee with no dependence on the size of potentially arbitrarily large state space. Furthermore, we also prove an $\Omega(\frac{\gamma^2}{1-\gamma} \sqrt{d A K})$ regret lower bound for this problem, showing that low-rank MDPs are statistically more difficult to learn than linear MDPs in the regret minimization setting. To the best of our knowledge, we present the first algorithm that interleaves representation learning, exploration, and exploitation to achieve the sublinear regret guarantee for RL with nonlinear function approximation and adversarial losses.

Knowledge tracing is a method used in education to assess and track the acquisition of knowledge by individual learners. It involves using a variety of techniques, such as quizzes, tests, and other forms of assessment, to determine what a learner knows and does not know about a particular subject. The goal of knowledge tracing is to identify gaps in understanding and provide targeted instruction to help learners improve their understanding and retention of material. This can be particularly useful in situations where learners are working at their own pace, such as in online learning environments. By providing regular feedback and adjusting instruction based on individual needs, knowledge tracing can help learners make more efficient progress and achieve better outcomes. Effectively solving the KT problem would unlock the potential of computer-aided education applications such as intelligent tutoring systems, curriculum learning, and learning materials recommendations. In this paper, we will present the results of the implementation of two Knowledge Tracing algorithms on a newly released dataset as part of the AAAI2023 Global Knowledge Tracing Challenge.

Causal discovery is becoming a key part in medical AI research. These methods can enhance healthcare by identifying causal links between biomarkers, demographics, treatments and outcomes. They can aid medical professionals in choosing more impactful treatments and strategies. In parallel, Large Language Models (LLMs) have shown great potential in identifying patterns and generating insights from text data. In this paper we investigate applying LLMs to the problem of determining the directionality of edges in causal discovery. Specifically, we test our approach on a deidentified set of Non Small Cell Lung Cancer(NSCLC) patients that have both electronic health record and genomic panel data. Graphs are validated using Bayesian Dirichlet estimators using tabular data. Our result shows that LLMs can accurately predict the directionality of edges in causal graphs, outperforming existing state-of-the-art methods. These findings suggests that LLMs can play a significant role in advancing causal discovery and help us better understand complex systems.

Language model (LM) prompting--a popular paradigm for solving NLP tasks-- has been shown to be susceptible to miscalibration and brittleness to slight prompt variations, caused by its discriminative prompting approach, i.e., predicting the label given the input. The framework is multivariate, as label descriptions allow us to seamlessly integrate additional contextual information about the labels to improve task performance. On various standard classification benchmarks, with six open-source LM families, we show that zero-shot classification with simple contextualization of the data source of the evaluation set consistently outperforms both zero-shot and few-shot baselines while improving robustness to prompt variations. Further, our approach enables personalizing classification in a zero-shot manner by incorporating author, subject, or reader information in the label descriptions. Language models, trained only on raw text, have been shown to perform new tasks simply by conditioning on a handful of demonstrations (Brown et al., 2020). Furthermore, ICL has been shown to be very sensitive to the choice of training examples, their order and format in the prompt (Lu et al., 2022; Sorensen et al., 2022) requiring major human effort to achieve optimal performance. In this work, we ask, "If the right demonstrations are challenging to find and only serve to implicitly prime the model, can we achieve the same performance zero-shot if we prime the language model explicitly in a robust way?" Our approach consists of two key ideas. First, most text classification methods follow a discriminative setup, which involves estimating the probability of the labels given the input, which can be sensitive to prompt or verbalizer variations. Instead, we use a generative setup, which involves estimating the probability of generating the input given different labels, which has been shown to have better worst-case performance (Min et al., 2022a).

Double-descent refers to the unexpected drop in test loss of a learning algorithm beyond an interpolating threshold with over-parameterization, which is not predicted by information criteria in their classical forms due to the limitations in the standard asymptotic approach. We update these analyses using the information risk minimization framework and provide Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for models learned by the Gibbs algorithm. Notably, the penalty terms for the Gibbs-based AIC and BIC correspond to specific information measures, i.e., symmetrized KL information and KL divergence. We extend this information-theoretic analysis to over-parameterized models by providing two different Gibbs-based BICs to compute the marginal likelihood of random feature models in the regime where the number of parameters $p$ and the number of samples $n$ tend to infinity, with $p/n$ fixed. Our experiments demonstrate that the Gibbs-based BIC can select the high-dimensional model and reveal the mismatch between marginal likelihood and population risk in the over-parameterized regime, providing new insights to understand double-descent.

Since the traffic administration at road intersections determines the capacity bottleneck of modern transportation systems, intelligent cooperative coordination for connected autonomous vehicles (CAVs) has shown to be an effective solution. In this paper, we try to formulate a Bi-Level CAV intersection coordination framework, where coordinators from High and Low levels are tightly coupled. In the High-Level coordinator where vehicles from multiple roads are involved, we take various metrics including throughput, safety, fairness and comfort into consideration. Motivated by the time consuming space-time resource allocation framework in [1], we try to give a low complexity solution by transforming the complicated original problem into a sequential linear programming one. Based on the "feasible tunnels" (FT) generated from the High-Level coordinator, we then propose a rapid gradient-based trajectory optimization strategy in the Low-Level planner, to effectively avoid collisions beyond High-level considerations, such as the pedestrian or bicycles. Simulation results and laboratory experiments show that our proposed method outperforms existing strategies. Moreover, the most impressive advantage is that the proposed strategy can plan vehicle trajectory in milliseconds, which is promising in realworld deployments. A detailed description include the coordination framework and experiment demo could be found at the supplement materials, or online at https://youtu.be/MuhjhKfNIOg.

Analysis of multivariate healthcare time series data is inherently challenging: irregular sampling, noisy and missing values, and heterogeneous patient groups with different dynamics violating exchangeability. In addition, interpretability and quantification of uncertainty are critically important. Here, we propose a novel class of models, a mixture of coupled hidden Markov models (M-CHMM), and demonstrate how it elegantly overcomes these challenges. To make the model learning feasible, we derive two algorithms to sample the sequences of the latent variables in the CHMM: samplers based on (i) particle filtering and (ii) factorized approximation. Compared to existing inference methods, our algorithms are computationally tractable, improve mixing, and allow for likelihood estimation, which is necessary to learn the mixture model. Experiments on challenging real-world epidemiological and semi-synthetic data demonstrate the advantages of the M-CHMM: improved data fit, capacity to efficiently handle missing and noisy measurements, improved prediction accuracy, and ability to identify interpretable subsets in the data.

There is an increase in interest to model driving maneuver patterns via the automatic unsupervised clustering of naturalistic sequential kinematic driving data. The patterns learned are often used in transportation research areas such as eco-driving, road safety, and intelligent vehicles. One such model capable of modeling these patterns is the Hierarchical Dirichlet Process Hidden Semi-Markov Model (HDP-HSMM), as it is often used to estimate data segmentation, state duration, and transition probabilities. While this model is a powerful tool for automatically clustering observed sequential data, the existing HDP-HSMM estimation suffers from an inherent tendency to overestimate the number of states. This can result in poor estimation, which can potentially impact impact transportation research through incorrect inference of driving patterns. In this paper, a new robust HDP-HSMM (rHDP-HSMM) method is proposed to reduce the number of redundant states and improve the consistency of the model's estimation. Both a simulation study and a case study using naturalistic driving data are presented to demonstrate the effectiveness of the proposed rHDP-HSMM in identifying and inference of driving maneuver patterns.

Although linear and quadratic discriminant analysis are widely recognized classical methods, they can encounter significant challenges when dealing with non-Gaussian distributions or contaminated datasets. This is primarily due to their reliance on the Gaussian assumption, which lacks robustness. We first explain and review the classical methods to address this limitation and then present a novel approach that overcomes these issues. In this new approach, the model considered is an arbitrary Elliptically Symmetrical (ES) distribution per cluster with its own arbitrary scale parameter. This flexible model allows for potentially diverse and independent samples that may not follow identical distributions. By deriving a new decision rule, we demonstrate that maximum-likelihood parameter estimation and classification are simple, efficient, and robust compared to state-of-the-art methods.

Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of applications ranging from science and engineering to quantitative finance. Despite this wide applicability in various fields, hardly any theoretical guarantees exist to justify the soundness of the maximum likelihood (ML) solution for this model. In fact, it is well known that the maximum likelihood estimation (MLE) can only recover the true model parameters up to a rotation. The main obstruction is posed by the inherent identifiability nature of the PPCA model resulting from the rotational symmetry of the parameterization. To resolve this ambiguity, we propose a novel approach using quotient topological spaces and in particular, we show that the maximum likelihood solution is consistent in an appropriate quotient Euclidean space. Furthermore, our consistency results encompass a more general class of estimators beyond the MLE. Strong consistency of the ML estimate and consequently strong covariance estimation of the PPCA model have also been established under a compactness assumption.