We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes.

We study a general clustering setting in which we have n elements to be clustered, and we aim to perform as few queries as possible to an oracle that returns a noisy sample of the weighted similarity between two elements. Our setting encompasses many application domains in which the similarity function is costly to compute and inherently noisy. We introduce two novel formulations of online learning problems rooted in the paradigm of Pure Exploration in Combinatorial Multi-Armed Bandits (PE-CMAB): fixed confidence and fixed budget settings. For both settings, we design algorithms that combine a sampling strategy with a classic approximation algorithm for correlation clustering and study their theoretical guarantees. Our results are the first examples of polynomial-time algorithms that work for the case of PE-CMAB in which the underlying offline optimization problem is NP-hard.

Particle-based Bayesian deep learning often requires a similarity metric to compare two networks. However, naive similarity metrics lack permutation invariance and are inappropriate for comparing networks. Centered Kernel Alignment (CKA) on feature kernels has been proposed to compare deep networks but has not been used as an optimization objective in Bayesian deep learning. In this paper, we explore the use of CKA in Bayesian deep learning to generate diverse ensembles and hypernetworks that output a network posterior. Noting that CKA projects kernels onto a unit hypersphere and that directly optimizing the CKA objective leads to diminishing gradients when two networks are very similar. We propose adopting the approach of hyperspherical energy (HE) on top of CKA kernels to address this drawback and improve training stability. Additionally, by leveraging CKA-based feature kernels, we derive feature repulsive terms applied to synthetically generated outlier examples. Experiments on both diverse ensembles and hypernetworks show that our approach significantly outperforms baselines in terms of uncertainty quantification in both synthetic and realistic outlier detection tasks.

Anomaly detection methods typically require fully observed data for model training and inference and cannot handle incomplete data, while the missing data problem is pervasive in science and engineering, leading to challenges in many important applications such as abnormal user detection in recommendation systems and novel or anomalous cell detection in bioinformatics, where the missing rates can be higher than 30% or even 80%. In this work, first, we construct and evaluate a straightforward strategy, "impute-then-detect", via combining state-of-the-art imputation methods with unsupervised anomaly detection methods, where the training data are composed of normal samples only. We observe that such twostage methods frequently yield imputation bias from normal data, namely, the imputation methods are inclined to make incomplete samples "normal", where the fundamental reason is that the imputation models learned only on normal data and cannot generalize well to abnormal data in the inference stage. To address this challenge, we propose an end-to-end method that integrates data imputation with anomaly detection into a unified optimization problem. The proposed model learns to generate well-designed pseudo-abnormal samples to mitigate the imputation bias and ensure the discrimination ability of both the imputation and detection processes. Furthermore, we provide theoretical guarantees for the effectiveness of the proposed method, proving that the proposed method can correctly detect anomalies with high probability. Experimental results on datasets with manually constructed missing values and inherent missing values demonstrate that our proposed method effectively mitigates the imputation bias and surpasses the baseline methods significantly.

We introduce a novel framework for incorporating human expertise into algorithmic predictions. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to predictive algorithms. We argue that this framing clarifies the problem of human-AI collaboration in prediction tasks, as experts often form judgments by drawing on information which is not encoded in an algorithm's training data. Algorithmic indistinguishability yields a natural test for assessing whether experts incorporate this kind of "side information", and further provides a simple but principled method for selectively incorporating human feedback into algorithmic predictions. We show that this method provably improves the performance of any feasible algorithmic predictor and precisely quantify this improvement. We find empirically that although algorithms often outperform their human counterparts on average, human judgment can improve algorithmic predictions on specific instances (which can be identified ex-ante). In an X-ray classification task, we find that this subset constitutes nearly 30% of the patient population. Our approach provides a natural way of uncovering this heterogeneity and thus enabling effective human-AI collaboration.

Despite the remarkable success of graph neural networks (GNNs) for graph representation learning, they are generally built on the (unreliable) i.i.d.

We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions, datatypes, and postulates) are relevant in proving a new theorem or carrying out a new construction. Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean. The collection includes the largest Lean 4 library Mathlib, and some of the largest Agda libraries: the standard library, the library of univalent mathematics Agda-unimath, and the TypeTopology library. Each data set represents the corresponding library in two ways: as a heterogeneous network, and as a list of s-expressions representing the syntax trees of all the entries in the library.