Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized observations are available. Specifically, consider $X_1$, $\tilde{X}_2$ and $X_3$ are observed variables, where $\tilde{X}_2$ is a discretization of latent variables $X_2$. Applying existing test methods to the observations of $X_1$, $\tilde{X}_2$ and $X_3$ can lead to a false conclusion about the underlying conditional independence of variables $X_1$, $X_2$ and $X_3$. Motivated by this, we propose a conditional independence test specifically designed to accommodate the presence of such discretization. To achieve this, we design the bridge equations to recover the parameter reflecting the statistical information of the underlying latent continuous variables. An appropriate test statistic and its asymptotic distribution under the null hypothesis of conditional independence have also been derived. Both theoretical results and empirical validation have been provided, demonstrating the effectiveness of our test methods.

In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such improvements were measured were accurately capturing the intended goal, whether the numerical differences in the resulting values were significant, or whether uncertainty played a role in this study and if it should have been taken into account, was of secondary importance. Whereas probability theory, be it frequentist or Bayesian, used to be the gold standard in science before the advent of the supercomputer, it was quickly replaced in favor of black box models and sheer computing power because of their ability to handle large data sets. This evolution sadly happened at the expense of interpretability and trustworthiness. However, while people are still trying to improve the predictive power of their models, the community is starting to realize that for many applications it is not so much the exact prediction that is of importance, but rather the variability or uncertainty. The work in this dissertation tries to further the quest for a world where everyone is aware of uncertainty, of how important it is and how to embrace it instead of fearing it. A specific, though general, framework that allows anyone to obtain accurate uncertainty estimates is singled out and analysed. Certain aspects and applications of the framework -- dubbed `conformal prediction' -- are studied in detail. Whereas many approaches to uncertainty quantification make strong assumptions about the data, conformal prediction is, at the time of writing, the only framework that deserves the title `distribution-free'. No parametric assumptions have to be made and the nonparametric results also hold without having to resort to the law of large numbers in the asymptotic regime.

The Adversarial Markov Decision Process (AMDP) is a learning framework that deals with unknown and varying tasks in decision-making applications like robotics and recommendation systems. A major limitation of the AMDP formalism, however, is pessimistic regret analysis results in the sense that although the cost function can change from one episode to the next, the evolution in many settings is not adversarial. To address this, we introduce and study a new variant of AMDP, which aims to minimize regret while utilizing a set of cost predictors. For this setting, we develop a new policy search method that achieves a sublinear optimistic regret with high probability, that is a regret bound which gracefully degrades with the estimation power of the cost predictors. Establishing such optimistic regret bounds is nontrivial given that (i) as we demonstrate, the existing importance-weighted cost estimators cannot establish optimistic bounds, and (ii) the feedback model of AMDP is different (and more realistic) than the existing optimistic online learning works. Our result, in particular, hinges upon developing a novel optimistically biased cost estimator that leverages cost predictors and enables a high-probability regret analysis without imposing restrictive assumptions. We further discuss practical extensions of the proposed scheme and demonstrate its efficacy numerically.

Automatic differentiation (see, for example, Ref.[1]) has revolutionized machine learning, permitting the routine application of gradient descent algorithms to fit to data models of essentially unlimited complexity. The same technology can be used to take the derivative of these models with respect to their inputs without the need to explicitly calculate the derivatives [2]. A potentially useful application of this capability is approximating the probability density function (pdf), f(x | θ), given an accurate neural network model of the associated conditional cumulative distribution function (cdf), F (x | θ), using the fact that F (x | θ) f(x | θ) =, (1) x where θ are the parameters of the data-generation mechanism, which we distinguish from the parameters w of the neural network model. This paper explores this possibility in the context of simulation-based frequentist inference [3-7]. Equation (1) furnishes an approximation of the pdf f(x | θ) whether x is a function of the underlying observations D only or if x = λ(D; θ) is a test statistic that depends on D as well as on the parameters θ. Moreover, computing the derivative of the cdf using autograd to obtain the pdf is exact; autograd does not use finite difference approximations.

Wildfires have significant impacts on global vegetation, wildlife, and humans. They destroy plant communities and wildlife habitats and contribute to increased emissions of carbon dioxide, nitrogen oxides, methane, and other pollutants. The prediction of wildfires relies on various independent variables combined with regression or machine learning methods. In this technical review, we describe the options for independent variables, data processing techniques, models, independent variables collinearity and importance estimation methods, and model performance evaluation metrics. First, we divide the independent variables into 4 aspects, including climate and meteorology conditions, socio-economical factors, terrain and hydrological features, and wildfire historical records. Second, preprocessing methods are described for different magnitudes, different spatial-temporal resolutions, and different formats of data. Third, the collinearity and importance evaluation methods of independent variables are also considered. Fourth, we discuss the application of statistical models, traditional machine learning models, and deep learning models in wildfire risk prediction. In this subsection, compared with other reviews, this manuscript particularly discusses the evaluation metrics and recent advancements in deep learning methods. Lastly, addressing the limitations of current research, this paper emphasizes the need for more effective deep learning time series forecasting algorithms, the utilization of three-dimensional data including ground and trunk fuel, extraction of more accurate historical fire point data, and improved model evaluation metrics.

Age-related language patterns play a crucial role in understanding linguistic differences and developing age-appropriate communication strategies. However, the lack of comprehensive and diverse datasets has hindered the progress of research in this area. To address this issue, we present TextAge, a curated text dataset that maps sentences to the age and age group of the producer, as well as an underage (under 13) label. TextAge covers a wide range of ages and includes both spoken and written data from various sources such as CHILDES, Meta, Poki Poems-by-kids, JUSThink, and the TV show "Survivor." The dataset undergoes extensive cleaning and preprocessing to ensure data quality and consistency. We demonstrate the utility of TextAge through two applications: Underage Detection and Generational Classification. For Underage Detection, we train a Naive Bayes classifier, fine-tuned RoBERTa, and XLNet models to differentiate between language patterns of minors and young-adults and over. For Generational Classification, the models classify language patterns into different age groups (kids, teens, twenties, etc.). The models excel at classifying the "kids" group but struggle with older age groups, particularly "fifties," "sixties," and "seventies," likely due to limited data samples and less pronounced linguistic differences. TextAge offers a valuable resource for studying age-related language patterns and developing age-sensitive language models. The dataset's diverse composition and the promising results of the classification tasks highlight its potential for various applications, such as content moderation, targeted advertising, and age-appropriate communication. Future work aims to expand the dataset further and explore advanced modeling techniques to improve performance on older age groups.

Predicting the remaining useful life (RUL) of ball bearings plays an important role in predictive maintenance. A common definition of the RUL is the time until a bearing is no longer functional, which we denote as an event, and many data-driven methods have been proposed to predict the RUL. However, few studies have addressed the problem of censored data, where this event of interest is not observed, and simply ignoring these observations can lead to an overestimation of the failure risk. In this paper, we propose a probabilistic estimation of RUL using survival analysis that supports censored data. First, we analyze sensor readings from ball bearings in the frequency domain and annotate when a bearing starts to deteriorate by calculating the Kullback-Leibler (KL) divergence between the probability density function (PDF) of the current process and a reference PDF. Second, we train several survival models on the annotated bearing dataset, capable of predicting the RUL over a finite time horizon using the survival function. This function is guaranteed to be strictly monotonically decreasing and is an intuitive estimation of the remaining lifetime. We demonstrate our approach in the XJTU-SY dataset using cross-validation and find that Random Survival Forests consistently outperforms both non-neural networks and neural networks in terms of the mean absolute error (MAE). Our work encourages the inclusion of censored data in predictive maintenance models and highlights the unique advantages that survival analysis offers when it comes to probabilistic RUL estimation and early fault detection.

Imitation learning is a promising paradigm for training robot control policies, but these policies can suffer from distribution shift, where the conditions at evaluation time differ from those in the training data. A popular approach for increasing policy robustness to distribution shift is interactive imitation learning (i.e., DAgger and variants), where a human operator provides corrective interventions during policy rollouts. However, collecting a sufficient amount of interventions to cover the distribution of policy mistakes can be burdensome for human operators. We propose IntervenGen (I-Gen), a novel data generation system that can autonomously produce a large set of corrective interventions with rich coverage of the state space from a small number of human interventions. We apply I-Gen to 4 simulated environments and 1 physical environment with object pose estimation error and show that it can increase policy robustness by up to 39x with only 10 human interventions. Videos and more results are available at https://sites.google.com/view/intervengen2024.

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: (1) We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. (2) We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. (3) Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.

To perform effective causal inference in high-dimensional datasets, initiating the process with causal discovery is imperative, wherein a causal graph is generated based on observational data. However, obtaining a complete and accurate causal graph poses a formidable challenge, recognized as an NP-hard problem. Recently, the advent of Large Language Models (LLMs) has ushered in a new era, indicating their emergent capabilities and widespread applicability in facilitating causal reasoning across diverse domains, such as medicine, finance, and science. The expansive knowledge base of LLMs holds the potential to elevate the field of causal reasoning by offering interpretability, making inferences, generalizability, and uncovering novel causal structures. In this paper, we introduce a new framework, named Autonomous LLM-Augmented Causal Discovery Framework (ALCM), to synergize data-driven causal discovery algorithms and LLMs, automating the generation of a more resilient, accurate, and explicable causal graph. The ALCM consists of three integral components: causal structure learning, causal wrapper, and LLM-driven causal refiner. These components autonomously collaborate within a dynamic environment to address causal discovery questions and deliver plausible causal graphs. We evaluate the ALCM framework by implementing two demonstrations on seven well-known datasets. Experimental results demonstrate that ALCM outperforms existing LLM methods and conventional data-driven causal reasoning mechanisms. This study not only shows the effectiveness of the ALCM but also underscores new research directions in leveraging the causal reasoning capabilities of LLMs.