To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and simplistic assumption is often violated in practice, which leads to unreliable inferences and uncertainty quantification. Unfortunately, existing methods for robustifying GPs break closed-form conditioning, which makes them less attractive to practitioners and significantly more computationally expensive. In this paper, we demonstrate how to perform provably robust and conjugate Gaussian process (RCGP) regression at virtually no additional cost using generalised Bayesian inference. RCGP is particularly versatile as it enables exact conjugate closed form updates in all settings where standard GPs admit them. To demonstrate its strong empirical performance, we deploy RCGP for problems ranging from Bayesian optimisation to sparse variational Gaussian processes.

Differentially private (DP) machine learning algorithms incur many sources of randomness, such as random initialization, random batch subsampling, and shuffling. However, such randomness is difficult to take into account when proving differential privacy bounds because it induces mixture distributions for the algorithm's output that are difficult to analyze. This paper focuses on improving privacy bounds for shuffling models and one-iteration differentially private gradient descent (DP-GD) with random initializations using $f$-DP. We derive a closed-form expression of the trade-off function for shuffling models that outperforms the most up-to-date results based on $(\epsilon,\delta)$-DP. Moreover, we investigate the effects of random initialization on the privacy of one-iteration DP-GD. Our numerical computations of the trade-off function indicate that random initialization can enhance the privacy of DP-GD. Our analysis of $f$-DP guarantees for these mixture mechanisms relies on an inequality for trade-off functions introduced in this paper. This inequality implies the joint convexity of $F$-divergences. Finally, we study an $f$-DP analog of the advanced joint convexity of the hockey-stick divergence related to $(\epsilon,\delta)$-DP and apply it to analyze the privacy of mixture mechanisms.

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding scenario within a given uncertainty set. However, existing work often resorts to some coarse relaxation of the uncertainty set for the sake of tractability, leading to overly conservative estimation of the policy value. In this paper, we propose a general estimator that provides a sharp lower bound of the policy value using convex programming. The generality of our estimator enables various extensions such as sensitivity analysis using f-divergence, model selection with cross validation and information criterion, and robust policy learning with the sharp lower bound. Furthermore, our estimation method can be reformulated as an empirical risk minimization problem thanks to the strong duality, which enables us to provide strong theoretical guarantees of the proposed estimator using M-estimation techniques.

The reverse engineering of a complex mixture, regardless of its nature, has become significant today. Being able to quickly assess the potential toxicity of new commercial products in relation to the environment presents a genuine analytical challenge. The development of digital tools (databases, chemometrics, machine learning, etc.) and analytical techniques (Raman spectroscopy, NIR spectroscopy, mass spectrometry, etc.) will allow for the identification of potential toxic molecules. In this article, we use the example of detergent products, whose composition can prove dangerous to humans or the environment, necessitating precise identification and quantification for quality control and regulation purposes. The combination of various digital tools (spectral database, mixture database, experimental design, Chemometrics / Machine Learning algorithm{\ldots}) together with different sample preparation methods (raw sample, or several concentrated / diluted samples) Raman spectroscopy, has enabled the identification of the mixture's constituents and an estimation of its composition. Implementing such strategies across different analytical tools can result in time savings for pollutant identification and contamination assessment in various matrices. This strategy is also applicable in the industrial sector for product or raw material control, as well as for quality control purposes.

We study pointwise estimation and uncertainty quantification for a sparse variational Gaussian process method with eigenvector inducing variables. For a rescaled Brownian motion prior, we derive theoretical guarantees and limitations for the frequentist size and coverage of pointwise credible sets. For sufficiently many inducing variables, we precisely characterize the asymptotic frequentist coverage, deducing when credible sets from this variational method are conservative and when overconfident/misleading. We numerically illustrate the applicability of our results and discuss connections with other common Gaussian process priors.

In an effort to further advance semi-supervised generative and classification tasks, we propose a simple yet effective training strategy called dual pseudo training (DPT), built upon strong semi-supervised learners and diffusion models. DPT operates in three stages: training a classifier on partially labeled data to predict pseudo-labels; training a conditional generative model using these pseudo-labels to generate pseudo images; and retraining the classifier with a mix of real and pseudo images. Empirically, DPT consistently achieves SOTA performance of semi-supervised generation and classification across various settings. In particular, with one or two labels per class, DPT achieves a Fr\'echet Inception Distance (FID) score of 3.08 or 2.52 on ImageNet 256x256. Besides, DPT outperforms competitive semi-supervised baselines substantially on ImageNet classification tasks, achieving top-1 accuracies of 59.0 (+2.8), 69.5 (+3.0), and 74.4 (+2.0) with one, two, or five labels per class, respectively. Notably, our results demonstrate that diffusion can generate realistic images with only a few labels (e.g., <0.1%) and generative augmentation remains viable for semi-supervised classification. Our code is available at https://github.com/ML-GSAI/DPT.

Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles. To enhance interpretability, our model involves a low-dimensional causal embedded space such that all the relevant causal information in the multivariate functional data is preserved in this lower-dimensional subspace. We prove that the proposed model is causally identifiable under standard assumptions that are often made in the causal discovery literature. To carry out inference of our model, we develop a fully Bayesian framework with suitable prior specifications and uncertainty quantification through posterior summaries. We illustrate the superior performance of our method over existing methods in terms of causal graph estimation through extensive simulation studies. We also demonstrate the proposed method using a brain EEG dataset.

Domain adaptation aims to transfer the knowledge learned on (data-rich) source domains to (low-resource) target domains, and a popular method is invariant representation learning, which matches and aligns the data distributions on the feature space. Although this method is studied extensively and applied on classification and regression problems, its adoption on ranking problems is sporadic, and the few existing implementations lack theoretical justifications. This paper revisits invariant representation learning for ranking. Upon reviewing prior work, we found that they implement what we call item-level alignment, which aligns the distributions of the items being ranked from all lists in aggregate but ignores their list structure. However, the list structure should be leveraged, because it is intrinsic to ranking problems where the data and the metrics are defined and computed on lists, not the items by themselves. To close this discrepancy, we propose list-level alignment -- learning domain-invariant representations at the higher level of lists. The benefits are twofold: it leads to the first domain adaptation generalization bound for ranking, in turn providing theoretical support for the proposed method, and it achieves better empirical transfer performance for unsupervised domain adaptation on ranking tasks, including passage reranking.

Large language models (LLMs) have complicated internal dynamics, but induce representations of words and phrases whose geometry we can study. Human language processing is also opaque, but neural response measurements can provide (noisy) recordings of activation during listening or reading, from which we can extract similar representations of words and phrases. Here we study the extent to which the geometries induced by these representations, share similarities in the context of brain decoding. We find that the larger neural language models get, the more their representations are structurally similar to neural response measurements from brain imaging. Code is available at https://github.com/coastalcph/

Passenger clustering based on trajectory records is essential for transportation operators. However, existing methods cannot easily cluster the passengers due to the hierarchical structure of the passenger trip information, including multiple trips within each passenger and multi-dimensional information about each trip. Furthermore, existing approaches rely on an accurate specification of the clustering number to start. Finally, existing methods do not consider spatial semantic graphs such as geographical proximity and functional similarity between the locations. In this paper, we propose a novel tensor Dirichlet Process Multinomial Mixture model with graphs, which can preserve the hierarchical structure of the multi-dimensional trip information and cluster them in a unified one-step manner with the ability to determine the number of clusters automatically. The spatial graphs are utilized in community detection to link the semantic neighbors. We further propose a tensor version of Collapsed Gibbs Sampling method with a minimum cluster size requirement. A case study based on Hong Kong metro passenger data is conducted to demonstrate the automatic process of cluster amount evolution and better cluster quality measured by within-cluster compactness and cross-cluster separateness. The code is available at https://github.com/bonaldli/TensorDPMM-G.