We develop an online learning MCMC approach applicable for hierarchical bayesian models and GLMS. We also develop a fat-tailed LTV model that generalizes over several kinds of fat and thin tails. We demonstrate both developments on commercial LTV data from a large mobile app.

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.

The outcome of all time series cannot be forecast, e.g. the flipping of a fair coin. Others, like the repeated {01} sequence {010101...} can be forecast exactly. Algorithmic information theory can provide a measure of forecastability that lies between these extremes. The degree of forecastability is a function of only the data. For prediction (or classification) of labeled data, we propose three categories for forecastability: oracle forecastability for predictions that are always exact, precise forecastability for errors up to a bound, and probabilistic forecastability for any other predictions. Examples are given in each case.

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.

In the realm of interpretability and out-of-distribution generalisation, the identifiability of latent variable models has emerged as a captivating field of inquiry. In this work, we delve into the identifiability of Switching Dynamical Systems, taking an initial stride toward extending identifiability analysis to sequential latent variable models. We first prove the identifiability of Markov Switching Models, which commonly serve as the prior distribution for the continuous latent variables in Switching Dynamical Systems. We present identification conditions for first-order Markov dependency structures, whose transition distribution is parametrised via non-linear Gaussians. We then establish the identifiability of the latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations, by leveraging identifiability analysis techniques from identifiable deep latent variable models. We finally develop estimation algorithms for identifiable Switching Dynamical Systems. Throughout empirical studies, we demonstrate the practicality of identifiable Switching Dynamical Systems for segmenting high-dimensional time series such as videos, and showcase the use of identifiable Markov Switching Models for regime-dependent causal discovery in climate data.