People are adept at learning a wide variety of structured patterns from small amounts of data, presenting a conundrum from the standpoint of the bias-variance tradeoff: what kinds of representations and algorithms support the joint flexibility and data-paucity of human learning? One possibility is that people "learn by programming": inducing probabilistic models to fit observed data. Here, we experimentally test human learning in the domain of structured 2-dimensional patterns, using a task in which participants repeatedly predicted where a dot would move based on its previous trajectory. We evaluate human performance against standard parametric and non-parametric time-series models, as well as two Bayesian program synthesis models whose hypotheses vary in their degree of structure: a compositional Gaussian Process model and a structured "Language of Thought" (LoT) model. We find that signatures of human pattern learning are best explained by the LoT model, supporting the idea that the flexibility and data-efficiency of human structure learning can be understood as probabilistic inference over an expressive space of programs.

Transformer-based architectures have recently exhibited remarkable successes across different domains beyond just powering large language models. However, existing approaches typically focus on predictive accuracy and computational cost, largely ignoring certain other practical issues such as robustness to contaminated samples. In this paper, by re-interpreting the self-attention mechanism as a non-parametric kernel density estimator, we adapt classical robust kernel density estimation methods to develop novel classes of transformers that are resistant to adversarial attacks and data contamination. We first propose methods that down-weight outliers in RKHS when computing the self-attention operations. We empirically show that these methods produce improved performance over existing state-of-the-art methods, particularly on image data under adversarial attacks.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations.

Many crucial biological processes rely on networks of protein-protein interactions. Predicting the effect of amino acid mutations on protein-protein binding is important in protein engineering, including therapeutic discovery. However, the scarcity of annotated experimental data on binding energy poses a significant challenge for developing computational approaches, particularly deep learning-based methods. In this work, we propose SidechainDiff, a novel representation learning-based approach that leverages unlabelled experimental protein structures. SidechainDiff utilizes a Riemannian diffusion model to learn the generative process of side-chain conformations and can also give the structural context representations of mutations on the protein-protein interface. Leveraging the learned representations, we achieve state-of-the-art performance in predicting the mutational effects on protein-protein binding.

Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live in some (often unknown) low-dimensional manifold embedded in a high-dimensional ambient space. The result is a modelling mismatch since -- by construction -- the invertibility requirement implies high-dimensional support of the learned distribution. Injective flows, mappings from low- to high-dimensional spaces, aim to fix this discrepancy by learning distributions on manifolds, but the resulting volume-change term becomes more challenging to evaluate. Current approaches either avoid computing this term entirely using various heuristics, or assume the manifold is known beforehand and therefore are not widely applicable.

An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated. However, errors are actually autocorrelated in many cases due to the temporality of the data, which makes such maximum likelihood estimations inaccurate. In this paper, in order to adjust for autocorrelated errors, we propose to learn the autocorrelation coefficient jointly with the model parameters. In our experiments, we verify the effectiveness of our approach on time series forecasting.

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by optimizing EBFlow with score-matching objectives, the computation of Jacobian determinants for linear transformations can be entirely bypassed. This feature enables the use of arbitrary linear layers in the construction of flow-based models without increasing the computational time complexity of each training iteration from \mathcal{O}(D 2L) to \mathcal{O}(D 3L) for an L -layered model that accepts D -dimensional inputs. This makes the training of EBFlow more efficient than the commonly-adopted maximum likelihood training method. In addition to the reduction in runtime, we enhance the training stability and empirical performance of EBFlow through a number of techniques developed based on our analysis of the score-matching methods.

One of the fundamental cognitive abilities of humans is to quickly resolve uncertainty by generating hypotheses and testing them via active trials. Encountering a novel phenomenon accompanied by ambiguous cause-effect relationships, humans make hypotheses against data, conduct inferences from observation, test their theory via experimentation, and correct the proposition if inconsistency arises. These iterative processes persist until the underlying mechanism becomes clear. In this work, we devise the IVRE (pronounced as "ivory") environment for evaluating artificial agents' reasoning ability under uncertainty. IVRE is an interactive environment featuring rich scenarios centered around Blicket detection.

Generative probabilistic modeling of biological sequences has widespread existing and potential use across biology and biomedicine, particularly given advances in high-throughput sequencing, synthesis and editing. However, we still lack methods with nucleotide resolution that are tractable at the scale of whole genomes and that can achieve high predictive accuracy in theory and practice. In this article we propose a new generative sequence model, the Bayesian embedded autoregressive (BEAR) model, which uses a parametric autoregressive model to specify a conjugate prior over a nonparametric Bayesian Markov model. We explore, theoretically and empirically, applications of BEAR models to a variety of statistical problems including density estimation, robust parameter estimation, goodness-of-fit tests, and two-sample tests. We prove rigorous asymptotic consistency results including nonparametric posterior concentration rates.

We consider density estimation for Besov spaces when the estimator is restricted to use only a limited number of bits about each sample. We provide a noninteractive adaptive estimator which exploits the sparsity of wavelet bases, along with a simulate-and-infer technique from parametric estimation under communication constraints. We show that our estimator is nearly rate-optimal by deriving minmax lower bounds that hold even when interactive protocols are allowed. Interestingly, while our wavelet-based estimator is almost rate-optimal for Sobolev spaces as well, it is unclear whether the standard Fourier basis, which arise naturally for those spaces, can be used to achieve the same performance.