Generalization error of spectral algorithms

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of $\textit{spectral algorithms}$ specified by profile $h(\lambda)$, and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile $h(\lambda)$ for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification

Large language models (LLMs) are notorious for hallucinating, i.e., producing erroneous claims in their output. Such hallucinations can be dangerous, as occasional factual inaccuracies in the generated text might be obscured by the rest of the output being generally factual, making it extremely hard for the users to spot them. Current services that leverage LLMs usually do not provide any means for detecting unreliable generations. Here, we aim to bridge this gap. In particular, we propose a novel fact-checking and hallucination detection pipeline based on token-level uncertainty quantification. Uncertainty scores leverage information encapsulated in the output of a neural network or its layers to detect unreliable predictions, and we show that they can be used to fact-check the atomic claims in the LLM output. Moreover, we present a novel token-level uncertainty quantification method that removes the impact of uncertainty about what claim to generate on the current step and what surface form to use. Our method Claim Conditioned Probability (CCP) measures only the uncertainty of particular claim value expressed by the model. Experiments on the task of biography generation demonstrate strong improvements for CCP compared to the baselines for six different LLMs and three languages. Human evaluation reveals that the fact-checking pipeline based on uncertainty quantification is competitive with a fact-checking tool that leverages external knowledge.

Predictive Uncertainty Quantification via Risk Decompositions for Strictly Proper Scoring Rules

Distinguishing sources of predictive uncertainty is of crucial importance in the application of forecasting models across various domains. Despite the presence of a great variety of proposed uncertainty measures, there are no strict definitions to disentangle them. Furthermore, the relationship between different measures of uncertainty quantification remains somewhat unclear. In this work, we introduce a general framework, rooted in statistical reasoning, which not only allows the creation of new uncertainty measures but also clarifies their interrelations. Our approach leverages statistical risk to distinguish aleatoric and epistemic uncertainty components and utilizes proper scoring rules to quantify them. To make it practically tractable, we propose an idea to incorporate Bayesian reasoning into this framework and discuss the properties of the proposed approximation.

Efficient Conformal Prediction under Data Heterogeneity

Conformal Prediction (CP) stands out as a robust framework for uncertainty quantification, which is crucial for ensuring the reliability of predictions. However, common CP methods heavily rely on data exchangeability, a condition often violated in practice. Existing approaches for tackling non-exchangeability lead to methods that are not computable beyond the simplest examples. This work introduces a new efficient approach to CP that produces provably valid confidence sets for fairly general non-exchangeable data distributions. We illustrate the general theory with applications to the challenging setting of federated learning under data heterogeneity between agents. Our method allows constructing provably valid personalized prediction sets for agents in a fully federated way. The effectiveness of the proposed method is demonstrated in a series of experiments on real-world datasets.

Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks

In modern federated learning, one of the main challenges is to account for inherent heterogeneity and the diverse nature of data distributions for different clients. This problem is often addressed by introducing personalization of the models towards the data distribution of the particular client. However, a personalized model might be unreliable when applied to the data that is not typical for this client. Eventually, it may perform worse for these data than the non-personalized global model trained in a federated way on the data from all the clients. This paper presents a new approach to federated learning that allows selecting a model from global and personalized ones that would perform better for a particular input point. It is achieved through a careful modeling of predictive uncertainties that helps to detect local and global in- and out-of-distribution data and use this information to select the model that is confident in a prediction. The comprehensive experimental evaluation on the popular real-world image datasets shows the superior performance of the model in the presence of out-of-distribution data while performing on par with state-of-the-art personalized federated learning algorithms in the standard scenarios.

LM-Polygraph: Uncertainty Estimation for Language Models

Recent advancements in the capabilities of large language models (LLMs) have paved the way for a myriad of groundbreaking applications in various fields. However, a significant challenge arises as these models often "hallucinate", i.e., fabricate facts without providing users an apparent means to discern the veracity of their statements. Uncertainty estimation (UE) methods are one path to safer, more responsible, and more effective use of LLMs. However, to date, research on UE methods for LLMs has been focused primarily on theoretical rather than engineering contributions. In this work, we tackle this issue by introducing LM-Polygraph, a framework with implementations of a battery of state-of-the-art UE methods for LLMs in text generation tasks, with unified program interfaces in Python. Additionally, it introduces an extendable benchmark for consistent evaluation of UE techniques by researchers, and a demo web application that enriches the standard chat dialog with confidence scores, empowering end-users to discern unreliable responses. LM-Polygraph is compatible with the most recent LLMs, including BLOOMz, LLaMA-2, ChatGPT, and GPT-4, and is designed to support future releases of similarly-styled LMs.

Selective Nonparametric Regression via Testing

Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much less developed. In this work, we consider the nonparametric heteroskedastic regression problem and develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor. We prove non-asymptotic bounds on the risk of the resulting estimator and show the existence of several different convergence regimes. Theoretical analysis is illustrated with a series of experiments on simulated and real-world data.

Optimal Estimation in Mixed-Membership Stochastic Block Models

Community detection is one of the most critical problems in modern network science. Its applications can be found in various fields, from protein modeling to social network analysis. Recently, many papers appeared studying the problem of overlapping community detection, where each node of a network may belong to several communities. In this work, we consider Mixed-Membership Stochastic Block Model (MMSB) first proposed by Airoldi et al. (2008). MMSB provides quite a general setting for modeling overlapping community structure in graphs. The central question of this paper is to reconstruct relations between communities given an observed network. We compare different approaches and establish the minimax lower bound on the estimation error. Then, we propose a new estimator that matches this lower bound. Theoretical results are proved under fairly general conditions on the considered model. Finally, we illustrate the theory in a series of experiments.

Conformal Prediction for Federated Uncertainty Quantification Under Label Shift

Federated Learning (FL) is a machine learning framework where many clients collaboratively train models while keeping the training data decentralized. Despite recent advances in FL, the uncertainty quantification topic (UQ) remains partially addressed. Among UQ methods, conformal prediction (CP) approaches provides distribution-free guarantees under minimal assumptions. We develop a new federated conformal prediction method based on quantile regression and take into account privacy constraints. This method takes advantage of importance weighting to effectively address the label shift between agents and provides theoretical guarantees for both valid coverage of the prediction sets and differential privacy. Extensive experimental studies demonstrate that this method outperforms current competitors.

Scalable Batch Acquisition for Deep Bayesian Active Learning

In deep active learning, it is especially important to choose multiple examples to markup at each step to work efficiently, especially on large datasets. At the same time, existing solutions to this problem in the Bayesian setup, such as BatchBALD, have significant limitations in selecting a large number of examples, associated with the exponential complexity of computing mutual information for joint random variables. We, therefore, present the Large BatchBALD algorithm, which gives a well-grounded approximation to the BatchBALD method that aims to achieve comparable quality while being more computationally efficient. We provide a complexity analysis of the algorithm, showing a reduction in computation time, especially for large batches. Furthermore, we present an extensive set of experimental results on image and text data, both on toy datasets and larger ones such as CIFAR-100.