We propose methods for density estimation and data synthesis using a novel form of unsupervised random forests. Inspired by generative adversarial networks, we implement a recursive procedure in which trees gradually learn structural properties of the data through alternating rounds of generation and discrimination. The method is provably consistent under minimal assumptions. Unlike classic tree-based alternatives, our approach provides smooth (un)conditional densities and allows for fully synthetic data generation. We achieve comparable or superior performance to state-of-the-art probabilistic circuits and deep learning models on various tabular data benchmarks while executing about two orders of magnitude faster on average. An accompanying $\texttt{R}$ package, $\texttt{arf}$, is available on $\texttt{CRAN}$.

This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and adaptive methods have been proposed to address the challenge of balancing model fidelity with size. Instead, state-of-the-art mapping approaches require tuning parameters for specific use cases, but do not generalize across diverse environments. To address this gap, we utilize a self-organizing principle from information-theoretic learning to automatically adapt the complexity of the GMM model based on the relevant information in the sensor data. The approach is evaluated against existing point cloud modeling techniques on real-world data with varying degrees of scene complexity.

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed curves, which often exhibit structural similarities at multiple levels. Modeling multiple closed curves in a way that efficiently incorporates such between-curve dependence remains a challenging problem. In this work, we propose and investigate a multiple-output (a.k.a. multi-output), multi-dimensional Gaussian process modeling framework. We illustrate the proposed methodological advances, and demonstrate the utility of meaningful uncertainty quantification, on several curve and shape-related tasks. This model-based approach not only addresses the problem of inference on closed curves (and their shapes) with kernel constructions, but also opens doors to nonparametric modeling of multi-level dependence for functional objects in general.

This paper presents two algorithms, AdaOFUL and VARA, for online sequential decision-making in the presence of heavy-tailed rewards with only finite variances. For linear stochastic bandits, we address the issue of heavy-tailed rewards by modifying the adaptive Huber regression and proposing AdaOFUL. AdaOFUL achieves a state-of-the-art regret bound of $\widetilde{O}\big(d\big(\sum_{t=1}^T \nu_{t}^2\big)^{1/2}+d\big)$ as if the rewards were uniformly bounded, where $\nu_{t}^2$ is the observed conditional variance of the reward at round $t$, $d$ is the feature dimension, and $\widetilde{O}(\cdot)$ hides logarithmic dependence. Building upon AdaOFUL, we propose VARA for linear MDPs, which achieves a tighter variance-aware regret bound of $\widetilde{O}(d\sqrt{HG^*K})$. Here, $H$ is the length of episodes, $K$ is the number of episodes, and $G^*$ is a smaller instance-dependent quantity that can be bounded by other instance-dependent quantities when additional structural conditions on the MDP are satisfied. Our regret bound is superior to the current state-of-the-art bounds in three ways: (1) it depends on a tighter instance-dependent quantity and has optimal dependence on $d$ and $H$, (2) we can obtain further instance-dependent bounds of $G^*$ under additional structural conditions on the MDP, and (3) our regret bound is valid even when rewards have only finite variances, achieving a level of generality unmatched by previous works. Overall, our modified adaptive Huber regression algorithm may serve as a useful building block in the design of algorithms for online problems with heavy-tailed rewards.

The Targeted Maximum Likelihood Estimation (TMLE) statistical data analysis framework integrates machine learning, statistical theory, and statistical inference to provide a least biased, efficient and robust strategy for estimation and inference of a variety of statistical and causal parameters. We describe and evaluate the epidemiological applications that have benefited from recent methodological developments. We conducted a systematic literature review in PubMed for articles that applied any form of TMLE in observational studies. We summarised the epidemiological discipline, geographical location, expertise of the authors, and TMLE methods over time. We used the Roadmap of Targeted Learning and Causal Inference to extract key methodological aspects of the publications. We showcase the contributions to the literature of these TMLE results. Of the 81 publications included, 25% originated from the University of California at Berkeley, where the framework was first developed by Professor Mark van der Laan. By the first half of 2022, 70% of the publications originated from outside the United States and explored up to 7 different epidemiological disciplines in 2021-22. Double-robustness, bias reduction and model misspecification were the main motivations that drew researchers towards the TMLE framework. Through time, a wide variety of methodological, tutorial and software-specific articles were cited, owing to the constant growth of methodological developments around TMLE. There is a clear dissemination trend of the TMLE framework to various epidemiological disciplines and to increasing numbers of geographical areas. The availability of R packages, publication of tutorial papers, and involvement of methodological experts in applied publications have contributed to an exponential increase in the number of studies that understood the benefits, and adoption, of TMLE.

Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases. In this letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting, finding a surprisingly small ID, of order 2. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high-dimensionality of sequences' space.

Several generic methods have recently been developed for change detection in heterogeneous remote sensing data, such as images from synthetic aperture radar (SAR) and multispectral radiometers. However, these are not well suited to detect weak signatures of certain disturbances of ecological systems. To resolve this problem we propose a new approach based on image-to-image translation and one-class classification (OCC). We aim to map forest mortality caused by an outbreak of geometrid moths in a sparsely forested forest-tundra ecotone using multisource satellite images. The images preceding and following the event are collected by Landsat-5 and RADARSAT-2, respectively. Using a recent deep learning method for change-aware image translation, we compute difference images in both satellites' respective domains. These differences are stacked with the original pre- and post-event images and passed to an OCC trained on a small sample from the targeted change class. The classifier produces a credible map of the complex pattern of forest mortality.

Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the partition function (i.e., the normalization of the density). This function can be easily calculated for simple low-dimensional problems but its computation is difficult or even intractable for general densities and high-dimensional problems. In this paper we propose an alternative approach based on Maximum A-Posteriori (MAP) estimators, we name Maximum Recovery MAP (MR-MAP), to derive estimators that do not require the computation of the partition function, and reformulate the problem as an optimization problem. We further propose a least-action type potential that allows us to quickly solve the optimization problem as a feed-forward hyperbolic neural network. We demonstrate the effectiveness of our methods on some standard data sets.

Current work on using visual analytics to determine causal relations among variables has mostly been based on the concept of counterfactuals. As such the derived static causal networks do not take into account the effect of time as an indicator. However, knowing the time delay of a causal relation can be crucial as it instructs how and when actions should be taken. Yet, similar to static causality, deriving causal relations from observational time-series data, as opposed to designed experiments, is not a straightforward process. It can greatly benefit from human insight to break ties and resolve errors. We hence propose a set of visual analytics methods that allow humans to participate in the discovery of causal relations associated with windows of time delay. Specifically, we leverage a well-established method, logic-based causality, to enable analysts to test the significance of potential causes and measure their influences toward a certain effect. Furthermore, since an effect can be a cause of other effects, we allow users to aggregate different temporal cause-effect relations found with our method into a visual flow diagram to enable the discovery of temporal causal networks. To demonstrate the effectiveness of our methods we constructed a prototype system named DOMINO and showcase it via a number of case studies using real-world datasets. Finally, we also used DOMINO to conduct several evaluations with human analysts from different science domains in order to gain feedback on the utility of our system in practical scenarios.

Abstract-- In this paper, we present an algorithm for learning time-correlated measurement covariances for application in batch state estimation. We parameterize the inverse measurement covariance matrix to be block-banded, which conveniently factorizes and results in a computationally efficient approach for correlating measurements across the entire trajectory. We train our covariance model through supervised learning using the groundtruth trajectory. In applications where the measurements are time-correlated, we demonstrate improved performance in both the mean posterior estimate and the covariance (i.e., improved estimator consistency). We verify that our proposed method results in a consistent In the research field of probabilistic robotics, we formulate batch estimator in a controlled simulation via a statistical test state estimation using probability theory in order to handle over several trials.