Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions.

Image captioning aims to describe visual content in natural language. As'a picture is worth a thousand words', there could be various correct descriptions for an image. However, with maximum likelihood estimation as the training objective, the captioning model is penalized whenever its prediction mismatches with the label. For instance, when the model predicts a word expressing richer semantics than the label, it will be penalized and optimized to prefer more concise expressions, referred to as conciseness optimization. In contrast, predictions that are more concise than labels lead to richness optimization. Such conflicting optimization directions could eventually result in the model generating general descriptions.

Some of the most successful knowledge graph embedding (KGE) models for link prediction – CP, RESCAL, TuckER, ComplEx – can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits – constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design.

In many scientific applications, we observe a system in different conditions in which its components may change, rather than in isolation. In our work, we are interested in explaining the generating process of such a multi-context system using a finite mixture of causal mechanisms. Recent work shows that this causal model is identifiable from data, but is limited to settings where the sparse mechanism shift hypothesis holds and only a subset of the causal conditionals change. As this assumption is not easily verifiable in practice, we study the more general principle that mechanism shifts are independent, which we formalize using the algorithmic notion of independence. We introduce an approach for causal discovery beyond partially directed graphs using Gaussian Process models, and give conditions under which we provably identify the correct causal model.

Regularization is one of the most fundamental topics in optimization, statistics and machine learning. To get sparsity in estimating a parameter u\in\mathbb{R} d, an \ell_q penalty term, \Vert u\Vert_q, is usually added to the objective function. What is the probabilistic distribution corresponding to such \ell_q penalty? What is the \emph{correct} stochastic process corresponding to \Vert u\Vert_q when we model functions u\in L q? This is important for statistically modeling high-dimensional objects such as images, with penalty to preserve certainty properties, e.g.

To take the esports scene to the next level, we introduce PandaSkill, a framework for assessing player performance and skill rating. Traditional rating systems like Elo and TrueSkill often overlook individual contributions and face challenges in professional esports due to limited game data and fragmented competitive scenes. PandaSkill leverages machine learning to estimate in-game player performance from individual player statistics. Each in-game role is modeled independently, ensuring a fair comparison between them. Then, using these performance scores, PandaSkill updates the player skill ratings using the Bayesian framework OpenSkill in a free-for-all setting. In this setting, skill ratings are updated solely based on performance scores rather than game outcomes, hightlighting individual contributions. To address the challenge of isolated rating pools that hinder cross-regional comparisons, PandaSkill introduces a dual-rating system that combines players' regional ratings with a meta-rating representing each region's overall skill level. Applying PandaSkill to five years of professional League of Legends matches worldwide, we show that our method produces skill ratings that better predict game outcomes and align more closely with expert opinions compared to existing methods.

While internet-scale data often comes in pairs (e.g., audio/image, image/text), we often want to perform inferences over modalities unseen together in the training data (e.g., audio/text). Empirically, this can often be addressed by learning multiple contrastive embedding spaces between existing modality pairs, implicitly hoping that unseen modality pairs will end up being aligned. This theoretical paper proves that this hope is well founded, under certain assumptions. Starting with the proper Bayesian approach of integrating out intermediate modalities, we show that directly comparing the representations of data from unpaired modalities can recover the same likelihood ratio. Our analysis builds on prior work on the geometry and probabilistic interpretation of contrastive representations, showing how these representations can answer many of the same inferences as probabilistic graphical models. Our analysis suggests two new ways of using contrastive representations: in settings with pre-trained contrastive models, and for handling language ambiguity in reinforcement learning. Our numerical experiments study the importance of our assumptions and demonstrate these new applications. Much of the appeal of contrastive learning is that it gives a "plug-n-play" approach for swapping one modality for another. Because representations from different modalities are trained to be aligned when representing the same object, the hope is that (say) a language representation and image representation of the same scene can be used as substitutes. This property is practically appealing for at least two reasons. First, it allows us to make use of pre-trained models. If you have a model that wants to make use of (say) language input and you have access to a pre-trained image-language contrastive model, you might simply train your model on the pre-trained image representations and hope that it will continue to work when you swap in the language representations.

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the interpretability of posterior predictive distributions. We demonstrate that under a discretized prior for the inner layer weights, we can exactly characterize the posterior predictive distribution as a Gaussian mixture. This setting allows us to define equivalence classes of network parameter values which produce the same likelihood (training error) and to relate the elements of these classes to the network's scaling regime -- defined via ratios of the training sample size, the size of each layer, and the number of final layer parameters. Of particular interest are distinct parameter realizations that map to low training error and yet correspond to distinct modes in the posterior predictive distribution. We identify settings that exhibit such predictive multimodality, and thus provide insight into the accuracy of unimodal posterior approximations. We also characterize the capacity of a model to "learn from data" by evaluating contraction of the posterior predictive in different scaling regimes.

Offline inverse reinforcement learning (Offline IRL) aims to recover the structure of rewards and environment dynamics that underlie observed actions in a fixed, finite set of demonstrations from an expert agent. Accurate models of expertise in executing a task has applications in safety-sensitive applications such as clinical decision making and autonomous driving. However, the structure of an expert's preferences implicit in observed actions is closely linked to the expert's model of the environment dynamics (i.e. the world''). Thus, inaccurate models of the world obtained from finite data with limited coverage could compound inaccuracy in estimated rewards. To address this issue, we propose a bi-level optimization formulation of the estimation task wherein the upper level is likelihood maximization based upon a conservative model of the expert's policy (lower level). The policy model is conservative in that it maximizes reward subject to a penalty that is increasing in the uncertainty of the estimated model of the world.

Training data attribution (TDA) techniques find influential training data for the model's prediction on the test data of interest. While conceptually useful, they are hardly applicable to deep models in practice, particularly because of their sensitivity to different model initialisation. In this paper, we introduce a Bayesian perspective on the TDA task, where the learned model is treated as a Bayesian posterior and the TDA estimates as random variables. From this novel viewpoint, we observe that the influence of an individual training sample is often overshadowed by the noise stemming from model initialisation and SGD batch composition. Based on this observation, we argue that TDA can only be reliably used for explaining deep model predictions that are consistently influenced by certain training data, independent of other noise factors.