Learned cardinality estimation methods have achieved high precision compared to traditional methods. Among learned methods, query-driven approaches have faced the workload drift problem for a long time. Although both data-driven and hybrid methods are proposed to avoid this problem, most of them suffer from high training and estimation costs, limited scalability, instability, and long-tail distribution problems on high-dimensional tables, which seriously affects the practical application of learned cardinality estimators. In this paper, we prove that most of these problems are directly caused by the widely used progressive sampling. We solve this problem by introducing predicate information into the autoregressive model and propose Duet, a stable, efficient, and scalable hybrid method to estimate cardinality directly without sampling or any non-differentiable process, which can not only reduce the inference complexity from $O(n)$ to $O(1)$ compared to Naru and UAE but also achieve higher accuracy on high cardinality and high-dimensional tables. Experimental results show that Duet can achieve all the design goals above and be much more practical. Besides, Duet even has a lower inference cost on CPU than that of most learned methods on GPU.

Non-autoregressive models have been widely studied in the Complete Information Scenario (CIS), in which the input has complete information of corresponding output. However, their explorations in the Incomplete Information Scenario (IIS) are extremely limited. Our analyses reveal that the IIS's incomplete input information will augment the inherent limitations of existing non-autoregressive models trained under Maximum Likelihood Estimation. In this paper, we propose for the IIS an Adversarial Non-autoregressive Transformer (ANT) which has two features: 1) Position-Aware Self-Modulation to provide more reasonable hidden representations, and 2) Dependency Feed Forward Network to strengthen its capacity in dependency modeling. We compare ANT with other mainstream models in the IIS and demonstrate that ANT can achieve comparable performance with much fewer decoding iterations. Furthermore, we show its great potential in various applications like latent interpolation and semi-supervised learning.

Binary phylogenetic trees inferred from biological data are central to understanding the shared evolutionary history of organisms. Inferring the placement of latent nodes in a tree by any optimality criterion (e.g., maximum likelihood) is an NP-hard problem, propelling the development of myriad heuristic approaches. Yet, these heuristics often lack a systematic means of uniformly sampling random trees or effectively exploring a tree space that grows factorially, which are crucial to optimisation problems such as machine learning. Phylo2Vec maps any binary tree with n leaves to an integer vector of length n 1. We prove that Phylo2Vec is both well-defined and bijective to the space of phylogenetic trees. The advantages of Phylo2Vec are twofold: i) easy uniform sampling of binary trees and ii) systematic ability to traverse tree space in very large or small jumps. As a proof of concept, we use Phylo2Vec for maximum likelihood inference on five real-world datasets and show that a simple hill climbing-based optimisation can efficiently traverse the vastness of tree space from a random to an optimal tree. Phylogenetic trees are a fundamental tool in depicting evolutionary processes, whether linguistic (evolution of different languages and language families) or biological (evolution of biological entities). In the latter field, phylogenetic trees are integral to multiple research domains, including evolution (Morlon et al., 2010), conservation (Rolland et al., 2011), and epidemiology, where they allow us to better understand infectious disease transmission dynamics (Ypma et al., 2013; Faria et al., 2021). A multitude of computer-readable formats have been proposed to store and represent (binary) phylogenetic trees. While basic data structures such as arrays or linked lists can be used for this purpose, the Newick format, as outlined by Olsen (1990) and Felsenstein (2004), has emerged as the standard notation. Each parenthesis encloses a pair of leaf nodes or subtrees, separated by a comma.

Human perception, memory and decision-making are impacted by tens of cognitive biases and heuristics that influence our actions and decisions. Despite the pervasiveness of such biases, they are generally not leveraged by today's Artificial Intelligence (AI) systems that model human behavior and interact with humans. In this theoretical paper, we claim that the future of human-machine collaboration will entail the development of AI systems that model, understand and possibly replicate human cognitive biases. We propose the need for a research agenda on the interplay between human cognitive biases and Artificial Intelligence. We categorize existing cognitive biases from the perspective of AI systems, identify three broad areas of interest and outline research directions for the design of AI systems that have a better understanding of our own biases.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

Regularization in modern machine learning is crucial, and it can take various forms in algorithmic design: training set, model family, error function, regularization terms, and optimizations. In particular, the learning rate, which can be interpreted as a temperature-like parameter within the statistical mechanics of learning, plays a crucial role in neural network training. Indeed, many widely adopted training strategies basically just define the decay of the learning rate over time. This process can be interpreted as decreasing a temperature, using either a global learning rate (for the entire model) or a learning rate that varies for each parameter. This paper proposes TempBalance, a straightforward yet effective layer-wise learning rate method. TempBalance is based on Heavy-Tailed Self-Regularization (HT-SR) Theory, an approach which characterizes the implicit self-regularization of different layers in trained models. We demonstrate the efficacy of using HT-SR-motivated metrics to guide the scheduling and balancing of temperature across all network layers during model training, resulting in improved performance during testing. We implement TempBalance on CIFAR10, CIFAR100, SVHN, and TinyImageNet datasets using ResNets, VGGs, and WideResNets with various depths and widths. Our results show that TempBalance significantly outperforms ordinary SGD and carefully-tuned spectral norm regularization. We also show that TempBalance outperforms a number of state-of-the-art optimizers and learning rate schedulers.

Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies and evolutionary distances on branches, is crucial for accurately inferring species relationships from molecular data and tasks requiring variable marginalization. Variational Bayesian methods are key to developing scalable, practical models; however, it remains challenging to conduct phylogenetic inference without restricting the combinatorially vast number of possible tree topologies. In this work, we introduce a novel, fully differentiable formulation of phylogenetic inference that leverages a unique representation of topological distributions in continuous geometric spaces. Through practical considerations on design spaces and control variates for gradient estimations, our approach, GeoPhy, enables variational inference without limiting the topological candidates. In experiments using real benchmark datasets, GeoPhy significantly outperformed other approximate Bayesian methods that considered whole topologies.

Our work presents a novel approach to shape optimization, with the twofold objective to improve the efficiency of global optimization algorithms while promoting the generation of high-quality designs during the optimization process free of geometrical anomalies. This is accomplished by reducing the number of the original design variables defining a new reduced subspace where the geometrical variance is maximized and modeling the underlying generative process of the data via probabilistic linear latent variable models such as factor analysis and probabilistic principal component analysis. We show that the data follows approximately a Gaussian distribution when the shape modification method is linear and the design variables are sampled uniformly at random, due to the direct application of the central limit theorem. The degree of anomalousness is measured in terms of Mahalanobis distance, and the paper demonstrates that abnormal designs tend to exhibit a high value of this metric. This enables the definition of a new optimization model where anomalous geometries are penalized and consequently avoided during the optimization loop. The procedure is demonstrated for hull shape optimization of the DTMB 5415 model, extensively used as an international benchmark for shape optimization problems. The global optimization routine is carried out using Bayesian optimization and the DIRECT algorithm. From the numerical results, the new framework improves the convergence of global optimization algorithms, while only designs with high-quality geometrical features are generated through the optimization routine thereby avoiding the wastage of precious computationally expensive simulations.

Artificial intelligence (AI) technology has become increasingly prevalent and transforms our everyday life. One important application of AI technology is the development of autonomous vehicles (AV). However, the reliability of an AV needs to be carefully demonstrated via an assurance test so that the product can be used with confidence in the field. To plan for an assurance test, one needs to determine how many AVs need to be tested for how many miles and the standard for passing the test. Existing research has made great efforts in developing reliability demonstration tests in the other fields of applications for product development and assessment. However, statistical methods have not been utilized in AV test planning. This paper aims to fill in this gap by developing statistical methods for planning AV reliability assurance tests based on recurrent events data. We explore the relationship between multiple criteria of interest in the context of planning AV reliability assurance tests. Specifically, we develop two test planning strategies based on homogeneous and non-homogeneous Poisson processes while balancing multiple objectives with the Pareto front approach. We also offer recommendations for practical use. The disengagement events data from the California Department of Motor Vehicles AV testing program is used to illustrate the proposed assurance test planning methods.

Next-generation radio interferometers like the Square Kilometer Array have the potential to unlock scientific discoveries thanks to their unprecedented angular resolution and sensitivity. One key to unlocking their potential resides in handling the deluge and complexity of incoming data. This challenge requires building radio interferometric imaging methods that can cope with the massive data sizes and provide high-quality image reconstructions with uncertainty quantification (UQ). This work proposes a method coined QuantifAI to address UQ in radio-interferometric imaging with data-driven (learned) priors for high-dimensional settings. Our model, rooted in the Bayesian framework, uses a physically motivated model for the likelihood. The model exploits a data-driven convex prior, which can encode complex information learned implicitly from simulations and guarantee the log-concavity of the posterior. We leverage probability concentration phenomena of high-dimensional log-concave posteriors that let us obtain information about the posterior, avoiding MCMC sampling techniques. We rely on convex optimisation methods to compute the MAP estimation, which is known to be faster and better scale with dimension than MCMC sampling strategies. Our method allows us to compute local credible intervals, i.e., Bayesian error bars, and perform hypothesis testing of structure on the reconstructed image. In addition, we propose a novel blazing-fast method to compute pixel-wise uncertainties at different scales. We demonstrate our method by reconstructing radio-interferometric images in a simulated setting and carrying out fast and scalable UQ, which we validate with MCMC sampling. Our method shows an improved image quality and more meaningful uncertainties than the benchmark method based on a sparsity-promoting prior. QuantifAI's source code: https://github.com/astro-informatics/QuantifAI.