We study the problem of causal structure learning from data using optimal transport (OT). Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional independence tests which are agnostic to the noise distribution. We provide an algorithm for causal discovery up to Markov Equivalence with no assumptions on the structural equations/noise distributions, which allows for settings with latent variables. Our approach also extends to score-based causal discovery by providing a novel means for defining scores. This allows us to uniquely recover the causal graph under additional identifiability and structural assumptions, such as additive noise or post-nonlinear models. We provide experimental results to compare the proposed approach with the state of the art on both synthetic and real-world datasets.

LGPs extend GPs to a large class of settings, including noisy, categorical, and count data. However, To achieve scalable and accurate inference for LGP inference is generally analytically intractable and latent Gaussian processes, we propose a variational hence requires approximations. In addition, direct GP inference approximation based on a family of Gaussian is prohibitive for large datasets due to cubic scaling distributions whose covariance matrices have in the data size. There are two main challenges for (L)GPs sparse inverse Cholesky (SIC) factors. We combine in many applications: One is to specify or learn a suitable this variational approximation of the posterior kernel for the GP, and the other is carrying out fast inference with a similar and efficient SIC-restricted for a given kernel. In this paper, we make no contributions Kullback-Leibler-optimal approximation of the to the former and instead focus on the latter challenge: We prior. We then focus on a particular SIC ordering assume that a parametric kernel form is given and propose and nearest-neighbor-based sparsity pattern an efficient approximation method for LGP inference via resulting in highly accurate prior and posterior structured variational learning.

Bayesian optimization (BO) primarily uses Gaussian processes (GP) as the key surrogate model, mostly with a simple stationary and separable kernel function such as the squared-exponential kernel with automatic relevance determination (SE-ARD). However, such simple kernel specifications are deficient in learning functions with complex features, such as being nonstationary, nonseparable, and multimodal. Approximating such functions using a local GP, even in a low-dimensional space, requires a large number of samples, not to mention in a high-dimensional setting. In this paper, we propose to use Bayesian Kernelized Tensor Factorization (BKTF) -- as a new surrogate model -- for BO in a $D$-dimensional Cartesian product space. Our key idea is to approximate the underlying $D$-dimensional solid with a fully Bayesian low-rank tensor CP decomposition, in which we place GP priors on the latent basis functions for each dimension to encode local consistency and smoothness. With this formulation, information from each sample can be shared not only with neighbors but also across dimensions. Although BKTF no longer has an analytical posterior, we can still efficiently approximate the posterior distribution through Markov chain Monte Carlo (MCMC) and obtain prediction and full uncertainty quantification (UQ). We conduct numerical experiments on both standard BO test functions and machine learning hyperparameter tuning problems, and our results show that BKTF offers a flexible and highly effective approach for characterizing complex functions with UQ, especially in cases where the initial sample size and budget are severely limited.

An assurance case is intended to provide justifiable confidence in the truth of its top claim, which typically concerns safety or security. A natural question is then "how much" confidence does the case provide? We argue that confidence cannot be reduced to a single attribute or measurement. Instead, we suggest it should be based on attributes that draw on three different perspectives: positive, negative, and residual doubts. Positive Perspectives consider the extent to which the evidence and overall argument of the case combine to make a positive statement justifying belief in its claims. We set a high bar for justification, requiring it to be indefeasible. The primary positive measure for this is soundness, which interprets the argument as a logical proof. Confidence in evidence can be expressed probabilistically and we use confirmation measures to ensure that the "weight" of evidence crosses some threshold. In addition, probabilities can be aggregated from evidence through the steps of the argument using probability logics to yield what we call probabilistic valuations for the claims. Negative Perspectives record doubts and challenges to the case, typically expressed as defeaters, and their exploration and resolution. Assurance developers must guard against confirmation bias and should vigorously explore potential defeaters as they develop the case, and should record them and their resolution to avoid rework and to aid reviewers. Residual Doubts: the world is uncertain so not all potential defeaters can be resolved. We explore risks and may deem them acceptable or unavoidable. It is crucial however that these judgments are conscious ones and that they are recorded in the assurance case. This report examines the perspectives in detail and indicates how Clarissa, our prototype toolset for Assurance 2.0, assists in their evaluation.

When factorized approximations are used for variational inference (VI), they tend to underestimate the uncertainty -- as measured in various ways -- of the distributions they are meant to approximate. We consider two popular ways to measure the uncertainty deficit of VI: (i) the degree to which it underestimates the componentwise variance, and (ii) the degree to which it underestimates the entropy. To better understand these effects, and the relationship between them, we examine an informative setting where they can be explicitly (and elegantly) analyzed: the approximation of a Gaussian,~$p$, with a dense covariance matrix, by a Gaussian,~$q$, with a diagonal covariance matrix. We prove that $q$ always underestimates both the componentwise variance and the entropy of $p$, \textit{though not necessarily to the same degree}. Moreover we demonstrate that the entropy of $q$ is determined by the trade-off of two competing forces: it is decreased by the shrinkage of its componentwise variances (our first measure of uncertainty) but it is increased by the factorized approximation which delinks the nodes in the graphical model of $p$. We study various manifestations of this trade-off, notably one where, as the dimension of the problem grows, the per-component entropy gap between $p$ and $q$ becomes vanishingly small even though $q$ underestimates every componentwise variance by a constant multiplicative factor. We also use the shrinkage-delinkage trade-off to bound the entropy gap in terms of the problem dimension and the condition number of the correlation matrix of $p$. Finally we present empirical results on both Gaussian and non-Gaussian targets, the former to validate our analysis and the latter to explore its limitations.

During crisis situations, social media allows people to quickly share information, including messages requesting help. This can be valuable to emergency responders, who need to categorise and prioritise these messages based on the type of assistance being requested. However, the high volume of messages makes it difficult to filter and prioritise them without the use of computational techniques. Fully supervised filtering techniques for crisis message categorisation typically require a large amount of annotated training data, but this can be difficult to obtain during an ongoing crisis and is expensive in terms of time and labour to create. This thesis focuses on addressing the challenge of low data availability when categorising crisis messages for emergency response. It first presents domain adaptation as a solution for this problem, which involves learning a categorisation model from annotated data from past crisis events (source domain) and adapting it to categorise messages from an ongoing crisis event (target domain). In many-to-many adaptation, where the model is trained on multiple past events and adapted to multiple ongoing events, a multi-task learning approach is proposed using pre-trained language models. This approach outperforms baselines and an ensemble approach further improves performance...

We study the phenomenon of \textit{in-context learning} (ICL) exhibited by large language models, where they can adapt to a new learning task, given a handful of labeled examples, without any explicit parameter optimization. Our goal is to explain how a pre-trained transformer model is able to perform ICL under reasonable assumptions on the pre-training process and the downstream tasks. We posit a mechanism whereby a transformer can achieve the following: (a) receive an i.i.d. sequence of examples which have been converted into a prompt using potentially-ambiguous delimiters, (b) correctly segment the prompt into examples and labels, (c) infer from the data a \textit{sparse linear regressor} hypothesis, and finally (d) apply this hypothesis on the given test example and return a predicted label. We establish that this entire procedure is implementable using the transformer mechanism, and we give sample complexity guarantees for this learning framework. Our empirical findings validate the challenge of segmentation, and we show a correspondence between our posited mechanisms and observed attention maps for step (c).

Autoregressive language models are trained by minimizing the cross-entropy of the model distribution Q relative to the data distribution P -- that is, minimizing the forward cross-entropy, which is equivalent to maximum likelihood estimation (MLE). We have observed that models trained in this way may "over-generalize", in the sense that they produce non-human-like text. Moreover, we believe that reverse cross-entropy, i.e., the cross-entropy of P relative to Q, is a better reflection of how a human would evaluate text generated by a model. Hence, we propose learning with MixCE, an objective that mixes the forward and reverse cross-entropies. We evaluate models trained with this objective on synthetic data settings (where P is known) and real data, and show that the resulting models yield better generated text without complex decoding strategies. Our code and models are publicly available at https://github.com/bloomberg/mixce-acl2023

Great storytellers know how to take us on a journey. They direct characters to act -- not necessarily in the most rational way -- but rather in a way that leads to interesting situations, and ultimately creates an impactful experience for audience members looking on. If audience experience is what matters most, then can we help artists and animators *directly* craft such experiences, independent of the concrete character actions needed to evoke those experiences? In this paper, we offer a novel computational framework for such tools. Our key idea is to optimize animations with respect to *simulated* audience members' experiences. To simulate the audience, we borrow an established principle from cognitive science: that human social intuition can be modeled as "inverse planning," the task of inferring an agent's (hidden) goals from its (observed) actions. Building on this model, we treat storytelling as "*inverse* inverse planning," the task of choosing actions to manipulate an inverse planner's inferences. Our framework is grounded in literary theory, naturally capturing many storytelling elements from first principles. We give a series of examples to demonstrate this, with supporting evidence from human subject studies.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.