publications

2025

1. AISTATS 2025

   All models are wrong, some are useful: Model Selection with Limited Labels

   Okanovic, Patrik, Kirsch, Andreas, Kasper, Jannes, Hoefler, Torsten, Krause, Andreas, and Gürel, Nezihe Merve

   AISTATS 2025 2025

   Abs arXiv HTML PDF

   We introduce MODEL SELECTOR, a framework for label-efficient selection of pretrained classifiers. Given a pool of unlabeled target data, MODEL SELECTOR samples a small subset of highly informative examples for labeling, in order to efficiently identify the best pretrained model for deployment on this target dataset. Through extensive experiments, we demonstrate that MODEL SELECTOR drastically reduces the need for labeled data while consistently picking the best or near-best performing model. Across 18 model collections on 16 different datasets, comprising over 1,500 pretrained models, MODEL SELECTOR reduces the labeling cost by up to 94.15% to identify the best model compared to the cost of the strongest baseline. Our results further highlight the robustness of MODEL SELECTOR in model selection, as it reduces the labeling cost by up to 72.41% when selecting a near-best model, whose accuracy is only within 1% of the best model.

2024

1. NeurIPS 2024

   Color-Filter: Conditional Loss Reduction Filtering for Targeted Language Model Pre-Training

   Brandfonbrener, David, Zhang, Hanlin, Kirsch, Andreas, Schwarz, Jonathan Richard, and Kakade, Sham

   In Advances in Neural Information Processing Systems 2024

   Abs arXiv HTML PDF

   Selecting high-quality data for pre-training is crucial in shaping the downstream task performance of language models. A major challenge lies in identifying this optimal subset, a problem generally considered intractable, thus necessitating scalable and effective heuristics. In this work, we propose a data selection method, CoLoR-Filter (Conditional Loss Reduction Filtering), which leverages an empirical Bayes-inspired approach to derive a simple and computationally efficient selection criterion based on the relative loss values of two auxiliary models. In addition to the modeling rationale, we evaluate CoLoR-Filter empirically on two language modeling tasks: (1) selecting data from C4 for domain adaptation to evaluation on Books and (2) selecting data from C4 for a suite of downstream multiple-choice question answering tasks. We demonstrate favorable scaling both as we subselect more aggressively and using small auxiliary models to select data for large target models. As one headline result, CoLoR-Filter data selected using a pair of 150m parameter auxiliary models can train a 1.2b parameter target model to match a 1.2b parameter model trained on 25b randomly selected tokens with 25x less data for Books and 11x less data for the downstream tasks.

2. ICLR Blogpost ’24

   Bayesian Model Selection: The Marginal Likelihood, Cross-Validation, and Conditional Log Marginal Likelihood

   Kirsch, Andreas

   In Third Blogpost Track at ICLR 2024

   Abs HTML Poster

   Bayesian model selection has long relied on the marginal likelihood and related quantities, often motivated by the principle of Occam’s razor. Following the paper ’Bayesian Model Selection, the Marginal Likelihood, and Generalization’ by Lotfi et al. (2022), this blog post critically examines the conventional focus on the marginal likelihood and related quantities for Bayesian model selection as a direct consequence of Occam’s razor. We find that the suitability of these criteria depends on the specific context and goals of the modeling task. We revisit the concepts of log marginal likelihood (LML), cross-validation, and the recently introduced conditional log marginal likelihood (CLML), highlighting their connections and differences through an information-theoretic lens. Through thought experiments and empirical observations, we explore the behavior of these model selection criteria in different data regimes under model misspecification and prior-data conflict, finding that the conditional marginal cross-entropy, closely related to cross-validation, is often more reliable for optimizing generalization performance. We review relevant literature, compare the CLML and validation loss for deep neural networks, and using a toy Bayesian linear regression, we demonstrate that all the discussed quantities can fail to reliably predict generalization. Our takeaways are that: there is no one-size-fits-all solution; the choice of model selection quantity depends on the specific context and goals; and in the future, we should take into account model complexity as well and not assume a uniform model prior. While this work leaves scope for more rigorous theoretical justification and more wide-ranging empirical investigation (along with deeper engagement with philosophical implications), it nevertheless provides grounds for questioning the primacy of the (conditional) log marginal likelihood and encourages critical thinking about its foundations, aiming for a more nuanced understanding of Bayesian model selection.

3. ICLR Blogpost ’24
   Highlight

   Bridging the Data Processing Inequality and Function-Space Variational Inference

   Kirsch, Andreas

   In Third Blogpost Track at ICLR 2024

   Abs HTML Poster

   This blog post explores the interplay between the Data Processing Inequality (DPI), a cornerstone concept in information theory, and Function-Space Variational Inference (FSVI) within the context of Bayesian deep learning. The DPI governs the transformation and flow of information through stochastic processes, and its unique connection to FSVI is employed to highlight FSVI’s focus on Bayesian predictive posteriors over parameter space. The post examines various forms of the DPI, including the KL divergence based DPI, and provides intuitive examples and detailed proofs. It also explores the equality case of the DPI to gain a deeper understanding. The connection between DPI and FSVI is then established, showing how FSVI can measure a predictive divergence independent of parameter symmetries. The post relates FSVI to knowledge distillation and label entropy regularization, highlighting the practical relevance of the theoretical concepts. Throughout the post, theoretical concepts are intertwined with intuitive explanations and mathematical rigor, offering a comprehensive understanding of these complex topics. By examining these concepts in depth, the post provides valuable insights for both theory and practice in machine learning.

2023

1. PhD Thesis

   Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions

   Kirsch, Andreas

   2023

   arXiv HTML PDF
2. TMLR

   Stochastic Batch Acquisition: A Simple Baseline for Deep Active Learning

   Kirsch, Andreas, Farquhar, Sebastian, Atighehchian, Parmida, Jesson, Andrew, Branchaud-Charron, Frédéric, and Gal, Yarin

   Transactions on Machine Learning Research 2023

   arXiv HTML PDF
3. TMLR

   Black-Box Batch Active Learning for Regression

   Kirsch, Andreas

   Transactions on Machine Learning Research 2023

   arXiv HTML PDF
4. CVPR 2023
   Highlight

   Deterministic Neural Networks with Appropriate Inductive Biases Capture Epistemic and Aleatoric Uncertainty

   Mukhoti*, Jishnu, Kirsch*, Andreas, van Amersfoort, Joost, Torr, Philip HS, and Gal, Yarin

   Conference on Computer Vision and Pattern Recognition 2023

   Abs arXiv HTML PDF

   We show that a single softmax neural net with minimal changes can beat the uncertainty predictions of Deep Ensembles and other more complex single-forward-pass uncertainty approaches. Standard softmax neural nets suffer from feature collapse and extrapolate arbitrarily for OoD points. This results in arbitrary softmax entropies for OoD points which can have high entropy, low, or anything in between, thus cannot capture epistemic uncertainty reliably. We prove that this failure lies at the core of "why" Deep Ensemble Uncertainty works well. Instead of using softmax entropy, we show that with appropriate inductive biases softmax neural nets trained with maximum likelihood reliably capture epistemic uncertainty through their feature-space density. This density is obtained using simple Gaussian Discriminant Analysis, but it cannot represent aleatoric uncertainty reliably. We show that it is necessary to combine feature-space density with softmax entropy to disentangle uncertainties well. We evaluate the epistemic uncertainty quality on active learning and OoD detection, achieving SOTA  98 AUROC on CIFAR-10 vs SVHN without fine-tuning on OoD data.

5. AISTATS 2023

   Prediction-Oriented Bayesian Active Learning

   Bickford Smith*, Freddie, Kirsch*, Andreas, Farquhar, Sebastian, Gal, Yarin, Foster, Adam, and Rainforth, Tom

   26th International Conference on Artificial Intelligence and Statistics 2023
6. Preprint

   Speeding Up BatchBALD: A k-BALD Family of Approximations for Active Learning

   Kirsch, Andreas

   arXiv 2023

   arXiv PDF
7. TMLR
   Repro. Cert.

   Does ’Deep Learning on a Data Diet’ reproduce? Overall yes, but GraNd at Initialization does not

   Kirsch, Andreas

   Transactions on Machine Learning Research (Reproducibility Certification) 2023

   arXiv HTML PDF

2022

1. TMLR

   A Note on ”Assessing Generalization of SGD via Disagreement”

   Kirsch, Andreas, and Gal, Yarin

   Transactions on Machine Learning Research 2022

   arXiv HTML PDF
2. TMLR

   Unifying Approaches in Active Learning and Active Sampling via Fisher Information and Information-Theoretic Quantities

   Kirsch, Andreas, and Gal, Yarin

   Transactions on Machine Learning Research 2022

   arXiv HTML PDF
3. Pre-training
   Workshop
   ICML 2022

   Plex: Towards reliability using pretrained large model extensions

   Tran, Dustin, Liu, Jeremiah, Dusenberry, Michael W, Phan, Du, Collier, Mark, Ren, Jie, Han, Kehang, Wang, Zi, Mariet, Zelda, Hu, Huiyi, and others,

   ICML Pre-training Workshop, 2022 2022

   arXiv HTML
4. ICML 2022

   Prioritized Training on Points that are Learnable, Worth Learning, and not yet Learnt

   Mindermann*, Sören, Brauner*, Jan M, Razzak*, Muhammed T, Sharma*, Mrinank, Kirsch, Andreas, Xu, Winnie, Höltgen, Benedikt, Gomez, Aidan N, Morisot, Adrien, Farquhar, Sebastian, and Gal, Yarin

   In Proceedings of the 39th International Conference on Machine Learning 2022

   arXiv HTML PDF
5. UpML 2022

   Marginal and Joint Cross-Entropies & Predictives for Online Bayesian Inference, Active Learning, and Active Sampling

   Kirsch, Andreas, Kossen, Jannik, and Gal, Yarin

   UpML 2022 – Updatable Machine Learning, Workshop @ ICML 2022 2022

   arXiv HTML PDF

2021

1. NeurIPS 2021

   Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data

   Jesson, Andrew, Tigas, Panagiotis, Amersfoort, Joost, Kirsch, Andreas, Shalit, Uri, and Gal, Yarin

   In Advances in Neural Information Processing Systems 2021

   arXiv HTML PDF
2. UDL 2021

   On Pitfalls in OoD Detection: Entropy Considered Harmful

   Kirsch, Andreas, Mukhoti, Jishnu, Amersfoort, Joost, Torr, Philip H.S., and Gal, Yarin

   In Uncertainty & Robustness in Deep Learning at Int. Conf. on Machine Learning (ICML Workshop) 2021

   Abs HTML PDF

   Entropy of a predictive distribution averaged over an ensemble or several posterior weight samples is often used as a metric for Out-of-Distribution (OoD) detection. However, we show that predictive entropy is inappropriate for this task because it mistakes ambiguous in-distribution samples as OoD. This issue remains hidden on curated datasets commonly used for benchmarking. We introduce a new dataset, Dirty-MNIST, with a long tail of ambiguous samples, which exemplifies this problem. Additionally, we look at the entropy of single, deterministic, softmax models and show that it is unreliable exactly for OoD samples. In summary, we caution against using predictive or softmax entropy for OoD detection in practice and introduce several methods to evaluate the quantitative difference between several uncertainty metrics.

3. UDL 2021

   Deterministic Neural Networks with Inductive Biases Capture Epistemic and Aleatoric Uncertainty

   Mukhoti, Jishnu, Kirsch, Andreas, Amersfoort, Joost, Torr, Philip H.S., and Gal, Yarin

   In Uncertainty & Robustness in Deep Learning at Int. Conf. on Machine Learning (ICML Workshop) 2021

   Abs HTML PDF

   We show that a single softmax neural net with minimal changes can beat the uncertainty predictions of Deep Ensembles and other more complex single-forward-pass uncertainty approaches. Standard softmax neural nets suffer from feature collapse and extrapolate arbitrarily for OoD points. This results in arbitrary softmax entropies for OoD points which can have high entropy, low, or anything in between, thus cannot capture epistemic uncertainty reliably. We prove that this failure lies at the core of "why" Deep Ensemble Uncertainty works well. Instead of using softmax entropy, we show that with appropriate inductive biases softmax neural nets trained with maximum likelihood reliably capture epistemic uncertainty through their feature-space density. This density is obtained using simple Gaussian Discriminant Analysis, but it cannot represent aleatoric uncertainty reliably. We show that it is necessary to combine feature-space density with softmax entropy to disentangle uncertainties well. We evaluate the epistemic uncertainty quality on active learning and OoD detection, achieving SOTA ∼ 98 AUROC on CIFAR-10 vs SVHN without fine-tuning on OoD data.

4. SubSetML 2021

   Active Learning under Pool Set Distribution Shift and Noisy Data

   Kirsch, Andreas, Rainforth, Tom, and Gal, Yarin

   In SubSetML: Subset Selection in Machine Learning: From Theory to Practice (ICML Workshop) 2021

   Abs arXiv PDF

   Active Learning is essential for more label-efficient deep learning. Bayesian Active Learning has focused on BALD, which reduces model parameter uncertainty. However, we show that BALD gets stuck on out-of-distribution or junk data that is not relevant for the task. We examine a novel *Expected Predictive Information Gain (EPIG)* to deal with distribution shifts of the pool set. EPIG reduces the uncertainty of *predictions* on an unlabelled *evaluation set* sampled from the test data distribution whose distribution might be different to the pool set distribution. Based on this, our new EPIG-BALD acquisition function for Bayesian Neural Networks selects samples to improve the performance on the test data distribution instead of selecting samples that reduce model uncertainty everywhere, including for out-of-distribution regions with low density in the test data distribution. Our method outperforms state-of-the-art Bayesian active learning methods on high-dimensional datasets and avoids out-of-distribution junk data in cases where current state-of-the-art methods fail.

5. SubSetML 2021

   A Simple Baseline for Batch Active Learning with Stochastic Acquisition Functions

   Kirsch, Andreas, Farquhar, Sebastian, and Gal, Yarin

   In SubSetML: Subset Selection in Machine Learning: From Theory to Practice (ICML Workshop) 2021

   Abs arXiv PDF

   In active learning, new labels are commonly acquired in batches. However, common acquisition functions are only meant for one-sample acquisition rounds at a time, and when their scores are used naively for batch acquisition, they result in batches lacking diversity, which deteriorates performance. On the other hand, state-of-the-art batch acquisition functions are costly to compute. In this paper, we present a novel class of stochastic acquisition functions that extend one-sample acquisition functions to the batch setting by observing how one-sample acquisition scores change as additional samples are acquired and modelling this difference for additional batch samples. We simply acquire new samples by sampling from the pool set using a Gibbs distribution based on the acquisition scores. Our acquisition functions are both vastly cheaper to compute and out-perform other batch acquisition functions.

6. SubSetML 2021

   A Practical & Unified Notation for Information-Theoretic Quantities in ML

   Kirsch, Andreas, and Gal, Yarin

   In SubSetML: Subset Selection in Machine Learning: From Theory to Practice (ICML Workshop) 2021

   Abs arXiv PDF

   Information theory is of importance to machine learning, but the notation for information-theoretic quantities is sometimes opaque. The right notation can convey valuable intuitions and concisely express new ideas. We propose such a notation for machine learning users and expand it to include information-theoretic quantities between events (outcomes) and random variables. We apply this notation to a popular information-theoretic acquisition function in Bayesian active learning which selects the most informative (unlabelled) samples to be labelled by an expert. We demonstrate the value of our notation when extending the acquisition function to the core-set problem, which consists of selecting the most informative samples given the labels.

7. SubSetML 2021

   Prioritized training on points that are learnable, worth learning, and not yet learned

   Mindermann, Sören, Razzak, Muhammed, Xu, Winnie, Kirsch, Andreas, Sharma, Mrinank, Morisot, Adrien, Gomez, Aidan N., Farquhar, Sebastian, Brauner, Jan, and Gal, Yarin

   In SubSetML: Subset Selection in Machine Learning: From Theory to Practice (ICML Workshop) 2021

   Abs HTML PDF

   Information theory is of importance to machine learning, but the notation for information-theoretic quantities is sometimes opaque. The right notation can convey valuable intuitions and concisely express new ideas. We propose such a notation for machine learning users and expand it to include information-theoretic quantities between events (outcomes) and random variables. We apply this notation to a popular information-theoretic acquisition function in Bayesian active learning which selects the most informative (unlabelled) samples to be labelled by an expert. We demonstrate the value of our notation when extending the acquisition function to the core-set problem, which consists of selecting the most informative samples given the labels.

8. NACI 2021

   Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data

   Jesson, Andrew, Tigas, Panagiotis, Amersfoort, Joost, Kirsch, Andreas, Shalit, Uri, and Gal, Yarin

   In The Neglected Assumptions In Causal Inference (ICML Workshop) 2021

   Abs arXiv HTML PDF

   Estimating personalized treatment effects from high-dimensional observational data is essential in situations where experimental designs are infeasible, unethical or expensive. Existing approaches rely on fitting deep models on outcomes observed for treated and control populations, but when measuring the outcome for an individual is costly (e.g. biopsy) a sample efficient strategy for acquiring outcomes is required. Deep Bayesian active learning provides a framework for efficient data acquisition by selecting points with high uncertainty. However, naive application of existing methods selects training data that is biased toward regions where the treatment effect cannot be identified because there is non-overlapping support between the treated and control populations. To maximize sample efficiency for learning personalized treatment effects, we introduce new acquisition functions grounded in information theory that bias data acquisition towards regions where overlap is satisfied, by combining insights from deep Bayesian active learning and causal inference. We demonstrate the performance of the proposed acquisition strategies on synthetic and semi-synthetic datasets IHDP and CMNIST and their extensions which aim to simulate common dataset biases and pathologies.

2020

1. UDL 2020

   Scalable Training with Information Bottleneck Objectives

   Kirsch, Andreas, Lyle, Clare, and Gal, Yarin

   In Uncertainty & Robustness in Deep Learning at Int. Conf. on Machine Learning (ICML Workshop) 2020

   Abs PDF

   The Information Bottleneck principle offers both a mechanism to explain how deep neural networks train and generalize, as well as a regularized objective with which to train models, with multiple competing objectives proposed in the literature. Moreover, the information-theoretic quantities used in these objectives are difficult to compute for large deep neural networks, often relying on density estimation using generative models. This, in turn, limits their use as a training objective. In this work, we review these quantities, compare and unify previously proposed objectives and relate them to surrogate objectives more friendly to optimization without relying on cumbersome tools such as density estimation. We find that these surrogate objectives allow us to apply the information bottleneck to modern neural network architectures with stochastic latent representations. We demonstrate our insights on MNIST and CIFAR10 with modern neural network architectures.

2. UDL 2020

   Learning CIFAR-10 with a Simple Entropy Estimator Using Information Bottleneck Objectives

   Kirsch, Andreas, Lyle, Clare, and Gal, Yarin

   In Uncertainty & Robustness in Deep Learning at Int. Conf. on Machine Learning (ICML Workshop) 2020

   Abs PDF

   The Information Bottleneck (IB) principle characterizes learning and generalization in deep neural networks in terms of the change in two information theoretic quantities and leads to a regularized objective function for training neural networks. These quantities are difficult to compute directly for deep neural networks. We show that it is possible to backpropagate through a simple entropy estimator to obtain an IB training method that works for modern neural network architectures. We evaluate our approach empirically on the CIFAR-10 dataset, showing that IB objectives can yield competitive performance on this dataset with a conceptually simple approach while also performing well against adversarial attacks out-of-the-box.

3. Preprint

   Unpacking Information Bottlenecks: Unifying Information-Theoretic Objectives in Deep Learning

   Kirsch, Andreas, Lyle, Clare, and Gal, Yarin

   arXiv Preprint 2020

   Abs arXiv PDF

   The Information Bottleneck principle offers both a mechanism to explain how deep neural networks train and generalize, as well as a regularized objective with which to train models. However, multiple competing objectives are proposed in the literature, and the information-theoretic quantities used in these objectives are difficult to compute for large deep neural networks, which in turn limits their use as a training objective. In this work, we review these quantities and compare and unify previously proposed objectives, which allows us to develop surrogate objectives more friendly to optimization without relying on cumbersome tools such as density estimation. We find that these surrogate objectives allow us to apply the information bottleneck to modern neural network architectures. We demonstrate our insights on MNIST, CIFAR-10 and Imagenette with modern DNN architectures (ResNets).

2019

1. NeurIPS 2019

   BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning

   Kirsch*, Andreas, van Amersfoort*, Joost, and Gal, Yarin

   NeurIPS 2019

   Abs HTML PDF

   We develop BatchBALD, a tractable approximation to the mutual information between a batch of points and model parameters, which we use as an acquisition function to select multiple informative points jointly for the task of deep Bayesian active learning. BatchBALD is a greedy linear-time 1-1/e-approximate algorithm amenable to dynamic programming and efficient caching. We compare BatchBALD to the commonly used approach for batch data acquisition and find that the current approach acquires similar and redundant points, sometimes performing worse than randomly acquiring data. We finish by showing that, using BatchBALD to consider dependencies within an acquisition batch, we achieve new state of the art performance on standard benchmarks, providing substantial data efficiency improvements in batch acquisition.