Point processes are powerful tools to model user activities and have a plethora of applications in social sciences. Predicting user activities based on point processes is a central problem. However, existing works are mostly problem specific, use heuristics, or simplify the stochastic nature of point processes. In this paper, we propose a framework that provides an efficient estimator of the probability mass function of point processes. In particular, we design a key reformulation of the prediction problem, and further derive a differential-difference equation to compute a conditional probability mass function. Our framework is applicable to general point processes and prediction tasks, and achieves superb predictive and efficiency performance in diverse real-world applications compared to the state of the art.

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs, which learn a distribution over weights, are currently the state-of-the-art for estimating predictive uncertainty; however these require significant modifications to the training procedure and are computationally expensive compared to standard (non-Bayesian) NNs. We propose an alternative to Bayesian NNs that is simple to implement, readily parallelizable, requires very little hyperparameter tuning, and yields high quality predictive uncertainty estimates. Through a series of experiments on classification and regression benchmarks, we demonstrate that our method produces well-calibrated uncertainty estimates which are as good or better than approximate Bayesian NNs. To assess robustness to dataset shift, we evaluate the predictive uncertainty on test examples from known and unknown distributions, and show that our method is able to express higher uncertainty on out-of-distribution examples. We demonstrate the scalability of our method by evaluating predictive uncertainty estimates on ImageNet.

Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network.

The last decade in deep learning has brought on increasingly capable systems that are deployed on a wide variety of applications. In natural language processing, the field has been transformed by a number of breakthroughs including large language models, which are used in increasingly many user-facing applications. In order to reap the benefits of this technology and reduce potential harms, it is important to quantify the reliability of model predictions and the uncertainties that shroud their development. This thesis studies how uncertainty in natural language processing can be characterized from a linguistic, statistical and neural perspective, and how it can be reduced and quantified through the design of the experimental pipeline. We further explore uncertainty quantification in modeling by theoretically and empirically investigating the effect of inductive model biases in text classification tasks. The corresponding experiments include data for three different languages (Danish, English and Finnish) and tasks as well as a large set of different uncertainty quantification approaches. Additionally, we propose a method for calibrated sampling in natural language generation based on non-exchangeable conformal prediction, which provides tighter token sets with better coverage of the actual continuation. Lastly, we develop an approach to quantify confidence in large black-box language models using auxiliary predictors, where the confidence is predicted from the input to and generated output text of the target model alone.

Representation learning on text-attributed graphs (TAGs) has attracted significant interest due to its wide-ranging real-world applications, particularly through Graph Neural Networks (GNNs). Traditional GNN methods focus on encoding the structural information of graphs, often using shallow text embeddings for node or edge attributes. This limits the model to understand the rich semantic information in the data and its reasoning ability for complex downstream tasks, while also lacking interpretability. With the rise of large language models (LLMs), an increasing number of studies are combining them with GNNs for graph representation learning and downstream tasks. While these approaches effectively leverage the rich semantic information in TAGs datasets, their main drawback is that they are only partially interpretable, which limits their application in critical fields. In this paper, we propose a verbalized graph representation learning (VGRL) method which is fully interpretable. In contrast to traditional graph machine learning models, which are usually optimized within a continuous parameter space, VGRL constrains this parameter space to be text description which ensures complete interpretability throughout the entire process, making it easier for users to understand and trust the decisions of the model. We conduct several studies to empirically evaluate the effectiveness of VGRL and we believe these method can serve as a stepping stone in graph representation learning.

The AlphaZero/MuZero (A/MZ) family of algorithms has achieved remarkable success across various challenging domains by integrating Monte Carlo Tree Search (MCTS) with learned models. Learned models introduce epistemic uncertainty, which is caused by learning from limited data and is useful for exploration in sparse reward environments. MCTS does not account for the propagation of this uncertainty however. To address this, we introduce Epistemic MCTS (EMCTS): a theoretically motivated approach to account for the epistemic uncertainty in search and harness the search for deep exploration. In the challenging sparse-reward task of writing code in the Assembly language subleq, AZ paired with our method achieves significantly higher sample efficiency over baseline AZ. Search with EMCTS solves variations of the commonly used hard-exploration benchmark Deep Sea - which baseline A/MZ are practically unable to solve - much faster than an otherwise equivalent method that does not use search for uncertainty estimation, demonstrating significant benefits from search for epistemic uncertainty estimation.

Posterior sampling in contextual bandits with a Gaussian prior can be implemented exactly or approximately using the Laplace approximation. The Gaussian prior is computationally efficient but it cannot describe complex distributions. In this work, we propose approximate posterior sampling algorithms for contextual bandits with a diffusion model prior. The key idea is to sample from a chain of approximate conditional posteriors, one for each stage of the reverse process, which are estimated in a closed form using the Laplace approximation. Our approximations are motivated by posterior sampling with a Gaussian prior, and inherit its simplicity and efficiency. They are asymptotically consistent and perform well empirically on a variety of contextual bandit problems.

We study the fundamental problem of sequential probability assignment, also known as online learning with logarithmic loss, with respect to an arbitrary, possibly nonparametric hypothesis class. Our goal is to obtain a complexity measure for the hypothesis class that characterizes the minimax regret and to determine a general, minimax optimal algorithm. Notably, the sequential $\ell_{\infty}$ entropy, extensively studied in the literature (Rakhlin and Sridharan, 2015, Bilodeau et al., 2020, Wu et al., 2023), was shown to not characterize minimax risk in general. Inspired by the seminal work of Shtarkov (1987) and Rakhlin, Sridharan, and Tewari (2010), we introduce a novel complexity measure, the \emph{contextual Shtarkov sum}, corresponding to the Shtarkov sum after projection onto a multiary context tree, and show that the worst case log contextual Shtarkov sum equals the minimax regret. Using the contextual Shtarkov sum, we derive the minimax optimal strategy, dubbed \emph{contextual Normalized Maximum Likelihood} (cNML). Our results hold for sequential experts, beyond binary labels, which are settings rarely considered in prior work. To illustrate the utility of this characterization, we provide a short proof of a new regret upper bound in terms of sequential $\ell_{\infty}$ entropy, unifying and sharpening state-of-the-art bounds by Bilodeau et al. (2020) and Wu et al. (2023).

Intracortical brain-computer interfaces (iBCIs) have allowed people with tetraplegia to control a computer cursor by imagining the movement of their paralyzed arm or hand. State-of-the-art decoders deployed in human iBCIs are derived from a Kalman filter that assumes Markov dynamics on the angle of intended movement, and a unimodal dependence on intended angle for each channel of neural activity. Due to errors made in the decoding of noisy neural data, as a user attempts to move the cursor to a goal, the angle between cursor and goal positions may change rapidly. We propose a dynamic Bayesian network that includes the on-screen goal position as part of its latent state, and thus allows the person's intended angle of movement to be aggregated over a much longer history of neural activity. This multiscale model explicitly captures the relationship between instantaneous angles of motion and long-term goals, and incorporates semi-Markov dynamics for motion trajectories. We also introduce a multimodal likelihood model for recordings of neural populations which can be rapidly calibrated for clinical applications. In offline experiments with recorded neural data, we demonstrate significantly improved prediction of motion directions compared to the Kalman filter. We derive an efficient online inference algorithm, enabling a clinical trial participant with tetraplegia to control a computer cursor with neural activity in real time. The observed kinematics of cursor movement are objectively straighter and smoother than prior iBCI decoding models without loss of responsiveness.

This paper studies the numerical computation of integrals, representing estimates or predictions, over the output f(x) of a computational model with respect to a distribution p(dx) over uncertain inputs x to the model. For the functional cardiac models that motivate this work, neither f nor p possess a closed-form expression and evaluation of either requires 100 CPU hours, precluding standard numerical integration methods. Our proposal is to treat integration as an estimation problem, with a joint model for both the a priori unknown function f and the a priori unknown distribution p. The result is a posterior distribution over the integral that explicitly accounts for dual sources of numerical approximation error due to a severely limited computational budget. This construction is applied to account, in a statistically principled manner, for the impact of numerical errors that (at present) are confounding factors in functional cardiac model assessment.