arXiv subjects

Bernhard Schölkopf

Publications and source records attributed to Bernhard Schölkopf.

At least 217 records · Page 12Linked to original sources

arXiv2023

Membership Inference Attacks against Language Models via Neighbourhood Comparison

Membership Inference attacks (MIAs) aim to predict whether a data sample was present in the training data of a machine learning model or not, and are widely used for assessing the privacy risks of language models. Most existing attacks rely on the observation that models tend to assign higher probabilities to their training samples than non-training points. However, simple thresholding of the model score in isolation tends to lead to high false-positive rates as it does not account for the intrinsic complexity of a sample. Recent work has demonstrated that reference-based attacks which compare model scores to those obtained from a reference model trained on similar data can substantially improve the performance of MIAs. However, in order to train reference models, attacks of this kind make the strong and arguably unrealistic assumption that an adversary has access to samples closely resembling the original training data. Therefore, we investigate their performance in more realistic scenarios and find that they are highly fragile in relation to the data distribution used to train reference models. To investigate whether this fragility provides a layer of safety, we propose and evaluate neighbourhood attacks, which compare model scores for a given sample to scores of synthetically generated neighbour texts and therefore eliminate the need for access to the training data distribution. We show that, in addition to being competitive with reference-based attacks that have perfect knowledge about the training data distribution, our attack clearly outperforms existing reference-free attacks as well as reference-based attacks with imperfect knowledge, which demonstrates the need for a reevaluation of the threat model of adversarial attacks.

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arXiv2023

Benchmarking Offline Reinforcement Learning on Real-Robot Hardware

Learning policies from previously recorded data is a promising direction for real-world robotics tasks, as online learning is often infeasible. Dexterous manipulation in particular remains an open problem in its general form. The combination of offline reinforcement learning with large diverse datasets, however, has the potential to lead to a breakthrough in this challenging domain analogously to the rapid progress made in supervised learning in recent years. To coordinate the efforts of the research community toward tackling this problem, we propose a benchmark including: i) a large collection of data for offline learning from a dexterous manipulation platform on two tasks, obtained with capable RL agents trained in simulation; ii) the option to execute learned policies on a real-world robotic system and a simulation for efficient debugging. We evaluate prominent open-sourced offline reinforcement learning algorithms on the datasets and provide a reproducible experimental setup for offline reinforcement learning on real systems.

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arXiv2023

Likelihood Annealing: Fast Calibrated Uncertainty for Regression

Recent advances in deep learning have shown that uncertainty estimation is becoming increasingly important in applications such as medical imaging, natural language processing, and autonomous systems. However, accurately quantifying uncertainty remains a challenging problem, especially in regression tasks where the output space is continuous. Deep learning approaches that allow uncertainty estimation for regression problems often converge slowly and yield poorly calibrated uncertainty estimates that can not be effectively used for quantification. Recently proposed post hoc calibration techniques are seldom applicable to regression problems and often add overhead to an already slow model training phase. This work presents a fast calibrated uncertainty estimation method for regression tasks called Likelihood Annealing, that consistently improves the convergence of deep regression models and yields calibrated uncertainty without any post hoc calibration phase. Unlike previous methods for calibrated uncertainty in regression that focus only on low-dimensional regression problems, our method works well on a broad spectrum of regression problems, including high-dimensional regression.Our empirical analysis shows that our approach is generalizable to various network architectures, including multilayer perceptrons, 1D/2D convolutional networks, and graph neural networks, on five vastly diverse tasks, i.e., chaotic particle trajectory denoising, physical property prediction of molecules using 3D atomistic representation, natural image super-resolution, and medical image translation using MRI.

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arXiv2023

Towards fully covariant machine learning

Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one possible representation to another. These are the passive symmetries; they include coordinate freedom, gauge symmetry, and units covariance, all of which have led to important results in physics. In machine learning, the most visible passive symmetry is the relabeling or permutation symmetry of graphs. Our goal is to understand the implications for machine learning of the many passive symmetries in play. We discuss dos and don'ts for machine learning practice if passive symmetries are to be respected. We discuss links to causal modeling, and argue that the implementation of passive symmetries is particularly valuable when the goal of the learning problem is to generalize out of sample. This paper is conceptual: It translates among the languages of physics, mathematics, and machine-learning. We believe that consideration and implementation of passive symmetries might help machine learning in the same ways that it transformed physics in the twentieth century.

stat.ML↗

arXiv2023

normflows: A PyTorch Package for Normalizing Flows

Normalizing flows model probability distributions through an expressive tractable density. They transform a simple base distribution, such as a Gaussian, through a sequence of invertible functions, which are referred to as layers. These layers typically use neural networks to become very expressive. Flows are ubiquitous in machine learning and have been applied to image generation, text modeling, variational inference, approximating Boltzmann distributions, and many other problems. Here, we present normflows, a Python package for normalizing flows. It allows to build normalizing flow models from a suite of base distributions, flow layers, and neural networks. The package is implemented in the popular deep learning framework PyTorch, which simplifies the integration of flows in larger machine learning models or pipelines. It supports most of the common normalizing flow architectures, such as Real NVP, Glow, Masked Autoregressive Flows, Neural Spline Flows, Residual Flows, and many more. The package can be easily installed via pip and the code is publicly available on GitHub.

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arXiv2023

Synchronizing Machine Learning Algorithms, Realtime Robotic Control and Simulated Environment with o80

Robotic applications require the integration of various modalities, encompassing perception, control of real robots and possibly the control of simulated environments. While the state-of-the-art robotic software solutions such as ROS 2 provide most of the required features, flexible synchronization between algorithms, data streams and control loops can be tedious. o80 is a versatile C++ framework for robotics which provides a shared memory model and a command framework for real-time critical systems. It enables expert users to set up complex robotic systems and generate Python bindings for scientists. o80's unique feature is its flexible synchronization between processes, including the traditional blocking commands and the novel ``bursting mode'', which allows user code to control the execution of the lower process control loop. This makes it particularly useful for setups that mix real and simulated environments.

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arXiv2023

Estimation Beyond Data Reweighting: Kernel Method of Moments

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a $φ$-divergence to an empirical distribution. However, the use of $φ$-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

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arXiv2023

Discrete Key-Value Bottleneck

Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has addressed this challenge involves pre-training of large encoders on volumes of readily available data, followed by task-specific tuning. Given a new task, however, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable key-value codes. Our paradigm will be to encode; process the representation via a discrete bottleneck; and decode. Here, the input is fed to the pre-trained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a sparse number of these key-value pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the discrete key-value bottleneck to minimize the effect of learning under distribution shifts and show that it reduces the complexity of the hypothesis class. We empirically verify the proposed method under challenging class-incremental learning scenarios and show that the proposed model - without any task boundaries - reduces catastrophic forgetting across a wide variety of pre-trained models, outperforming relevant baselines on this task.

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arXiv2023

Causal Effect Estimation from Observational and Interventional Data Through Matrix Weighted Linear Estimators

We study causal effect estimation from a mixture of observational and interventional data in a confounded linear regression model with multivariate treatments. We show that the statistical efficiency in terms of expected squared error can be improved by combining estimators arising from both the observational and interventional setting. To this end, we derive methods based on matrix weighted linear estimators and prove that our methods are asymptotically unbiased in the infinite sample limit. This is an important improvement compared to the pooled estimator using the union of interventional and observational data, for which the bias only vanishes if the ratio of observational to interventional data tends to zero. Studies on synthetic data confirm our theoretical findings. In settings where confounding is substantial and the ratio of observational to interventional data is large, our estimators outperform a Stein-type estimator and various other baselines.

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arXiv2023

A Causal Framework to Quantify the Robustness of Mathematical Reasoning with Language Models

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

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arXiv2023

Stochastic Marginal Likelihood Gradients using Neural Tangent Kernels

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

stat.ML↗

arXiv2023

On the Identifiability and Estimation of Causal Location-Scale Noise Models

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect $Y$ can be written as a function of the cause $X$ and a noise source $N$ independent of $X$, which may be scaled by a positive function $g$ over the cause, i.e., $Y = f(X) + g(X)N$. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of $Y$ given $X$ as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

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arXiv2023

Delphic Offline Reinforcement Learning under Nonidentifiable Hidden Confounding

A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding: unobserved variables may influence both the actions taken by the agent and the observed outcomes. Hidden confounding can compromise the validity of any causal conclusion drawn from data and presents a major obstacle to effective offline RL. In the present paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to hidden confounding bias, termed delphic uncertainty, which uses variation over world models compatible with the observations, and differentiate it from the well-known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as on electronic health records. Our results suggest that nonidentifiable hidden confounding bias can be mitigated to improve offline RL solutions in practice.

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arXiv2023

Group equivariant neural posterior estimation

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

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arXiv2023

Real-time gravitational-wave science with neural posterior estimation

We demonstrate unprecedented accuracy for rapid gravitational-wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational-wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from O(day) to a minute per event. Our networks are trained using simulated data, including an estimate of the detector-noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters, and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm -- called "DINGO" -- sets a new standard in fast-and-accurate inference of physical parameters of detected gravitational-wave events, which should enable real-time data analysis without sacrificing accuracy.

gr-qc↗

arXiv2023

Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference

We combine amortized neural posterior estimation with importance sampling for fast and accurate gravitational-wave inference. We first generate a rapid proposal for the Bayesian posterior using neural networks, and then attach importance weights based on the underlying likelihood and prior. This provides (1) a corrected posterior free from network inaccuracies, (2) a performance diagnostic (the sample efficiency) for assessing the proposal and identifying failure cases, and (3) an unbiased estimate of the Bayesian evidence. By establishing this independent verification and correction mechanism we address some of the most frequent criticisms against deep learning for scientific inference. We carry out a large study analyzing 42 binary black hole mergers observed by LIGO and Virgo with the SEOBNRv4PHM and IMRPhenomXPHM waveform models. This shows a median sample efficiency of $\approx 10\%$ (two orders-of-magnitude better than standard samplers) as well as a ten-fold reduction in the statistical uncertainty in the log evidence. Given these advantages, we expect a significant impact on gravitational-wave inference, and for this approach to serve as a paradigm for harnessing deep learning methods in scientific applications.

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arXiv2023

Provably Learning Object-Centric Representations

Learning structured representations of the visual world in terms of objects promises to significantly improve the generalization abilities of current machine learning models. While recent efforts to this end have shown promising empirical progress, a theoretical account of when unsupervised object-centric representation learning is possible is still lacking. Consequently, understanding the reasons for the success of existing object-centric methods as well as designing new theoretically grounded methods remains challenging. In the present work, we analyze when object-centric representations can provably be learned without supervision. To this end, we first introduce two assumptions on the generative process for scenes comprised of several objects, which we call compositionality and irreducibility. Under this generative process, we prove that the ground-truth object representations can be identified by an invertible and compositional inference model, even in the presence of dependencies between objects. We empirically validate our results through experiments on synthetic data. Finally, we provide evidence that our theory holds predictive power for existing object-centric models by showing a close correspondence between models' compositionality and invertibility and their empirical identifiability.

cs.LG↗

arXiv2023

All Roads Lead to Rome? Exploring the Invariance of Transformers' Representations

Transformer models bring propelling advances in various NLP tasks, thus inducing lots of interpretability research on the learned representations of the models. However, we raise a fundamental question regarding the reliability of the representations. Specifically, we investigate whether transformers learn essentially isomorphic representation spaces, or those that are sensitive to the random seeds in their pretraining process. In this work, we formulate the Bijection Hypothesis, which suggests the use of bijective methods to align different models' representation spaces. We propose a model based on invertible neural networks, BERT-INN, to learn the bijection more effectively than other existing bijective methods such as the canonical correlation analysis (CCA). We show the advantage of BERT-INN both theoretically and through extensive experiments, and apply it to align the reproduced BERT embeddings to draw insights that are meaningful to the interpretability research. Our code is at https://github.com/twinkle0331/BERT-similarity.

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