ICML 2023 论文列表

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

Deep reinforcement learning (RL) is a powerful approach for solving optimal control problems. However, RL-trained policies often suffer from the action fluctuation problem, where the consecutive actions significantly differ despite only slight state variations. This problem results in mechanical components' wear and tear and poses safety hazards. The action fluctuation is caused by the high Lipschitz constant of actor networks. To address this problem, we propose a neural network named LipsNet. We propose the Multi-dimensional Gradient Normalization (MGN) method, to constrain the Lipschitz constant of networks with multi-dimensional input and output. Benefiting from MGN, LipsNet achieves Lipschitz continuity, allowing smooth actions while preserving control performance by adjusting Lipschitz constant. LipsNet addresses the action fluctuation problem at network level rather than algorithm level, which can serve as actor networks in most RL algorithms, making it more flexible and user-friendly than previous works. Experiments demonstrate that LipsNet has good landscape smoothness and noise robustness, resulting in significantly smoother action compared to the Multilayer Perceptron.

We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$ for three symmetry groups that are missing from the machine learning literature: $O(n)$, the orthogonal group; $SO(n)$, the special orthogonal group; and $Sp(n)$, the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$ when the group is $O(n)$ or $SO(n)$, and in the symplectic basis of $\mathbb{R}^{n}$ when the group is $Sp(n)$.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as *properness*, which asserts that Bayes' rule is optimal. Recent works have sought to *learn losses* and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps $\mathbb{R}$ to $[0,1]$ to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between $\mathbb{R}^{C-1}$ and the projected probability simplex $\tilde{\Delta}^{C-1}$ by using monotonicity of gradients of convex functions. We present LegendreTron as a novel and practical method that jointly learns *proper canonical losses* and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a $t$-test at 99% significance on all datasets with greater than $10$ classes.

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we propose a new adversarial training algorithm that is theoretically well motivated and empirically superior to other existing algorithms. A novel feature of the proposed algorithm is to apply more regularization to data vulnerable to adversarial attacks than other existing regularization algorithms do. Theoretically, we show that our algorithm can be understood as an algorithm of minimizing a newly derived upper bound of the robust risk. Numerical experiments illustrate that our proposed algorithm improves the generalization (accuracy on examples) and robustness (accuracy on adversarial attacks) simultaneously to achieve the state-of-the-art performance.

Providing generalization guarantees for modern neural networks has been a crucial task in statistical learning. Recently, several studies have attempted to analyze the generalization error in such settings by using tools from fractal geometry. While these works have successfully introduced new mathematical tools to apprehend generalization, they heavily rely on a Lipschitz continuity assumption, which in general does not hold for neural networks and might make the bounds vacuous. In this work, we address this issue and prove fractal geometry-based generalization bounds without requiring any Lipschitz assumption. To achieve this goal, we build up on a classical covering argument in learning theory and introduce a data-dependent fractal dimension. Despite introducing a significant amount of technical complications, this new notion lets us control the generalization error (over either fixed or random hypothesis spaces) along with certain mutual information (MI) terms. To provide a clearer interpretation to the newly introduced MI terms, as a next step, we introduce a notion of `geometric stability' and link our bounds to the prior art. Finally, we make a rigorous connection between the proposed data-dependent dimension and topological data analysis tools, which then enables us to compute the dimension in a numerically efficient way. We support our theory with experiments conducted on various settings.

This paper revisits Gaussian Mixture Copula Model (GMCM), a more expressive alternative to the widely used Gaussian Mixture Model (GMM), with the goal to make its parameter estimation tractable. Both the Expectation Maximization and the direct Likelihood Maximization frameworks for GMCM have to grapple with a likelihood function that lacks a closed form. This has led to a few approximation schemes that alleviate the problem, nonetheless leaving the issue still unresolved. Additionally, past works have alluded to an additional challenge of parameter non-identifiability, but none has offered a rigorous treatment and a commensurate solution framework to overcome the same. This work offers solutions to each of these issues in an attempt to help GMCM realize its full potential. The source of non-identifiability is not only proven but also suitable priors are proposed that eliminate the problem. Additionally, an efficient numerical framework is proposed to evaluate the intractable likelihood function, while also providing its analytical derivatives. Finally, a view of GMCM as a series of bijective mappings from a base distribution is presented, which paves the way to synthesize GMCM using modern, probabilistic programming languages (PPLs). The main claims of this work are supported by empirical evidence gathered on synthetic and real-world datasets.

Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower dimensions. In this paper, we propose a novel sketching scheme for the first order method in large-scale distributed learning setting, such that the communication costs between distributed agents are saved while the convergence of the algorithms is still guaranteed. Given gradient information in a high dimension $d$, the agent passes the compressed information processed by a sketching matrix $R\in \mathbb{R}^{s\times d}$ with $s\ll d$, and the receiver de-compressed via the de-sketching matrix $R^\top$ to ``recover'' the information in original dimension. Using such a framework, we develop algorithms for federated learning with lower communication costs. However, such random sketching does not protect the privacy of local data directly. We show that the gradient leakage problem still exists after applying the sketching technique by presenting a specific gradient attack method. As a remedy, we prove rigorously that the algorithm will be differentially private by adding additional random noises in gradient information, which results in a both communication-efficient and differentially private first order approach for federated learning tasks. Our sketching scheme can be further generalized to other learning settings and might be of independent interest itself.

This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limited expressive capabilities of the individual network itself. Specifically, we prove by construction that $\mathcal{L}_2\circ \boldsymbol{g}^{\circ r}\circ \boldsymbol{\mathcal{L}}_1$ can approximate $1$-Lipschitz continuous functions on $[0,1]^d$ with an error $\mathcal{O}(r^{-1/d})$, where $\boldsymbol{g}$ is realized by a fixed-size ReLU network, $\boldsymbol{\mathcal{L}}_1$ and $\mathcal{L}_2$ are two affine linear maps matching the dimensions, and $\boldsymbol{g}^{\circ r}$ denotes the $r$-times composition of $\boldsymbol{g}$. Furthermore, we extend such a result to generic continuous functions on $[0,1]^d$ with the approximation error characterized by the modulus of continuity. Our results reveal that a continuous-depth network generated via a dynamical system has immense approximation power even if its dynamics function is time-independent and realized by a fixed-size ReLU network.

In this paper, we propose a novel tree-based algorithm named *Extrapolated Random Tree for Regression* (ERTR) that adapts to arbitrary smoothness of the regression function while maintaining the interpretability of the tree. We first put forward the *homothetic random tree for regression* (HRTR) that converges to the target function as the homothetic ratio approaches zero. Then ERTR uses a linear regression model to extrapolate HRTR estimations with different ratios to the ratio zero. From the theoretical perspective, we for the first time establish the optimal convergence rates for ERTR when the target function resides in the general Hölder space $C^{k,\alpha}$ for $k\in \mathbb{N}$, whereas the lower bound of the convergence rate of the random tree for regression (RTR) is strictly slower than ERTR in the space $C^{k,\alpha}$ for $k\geq 1$. This shows that ERTR outperforms RTR for the target function with high-order smoothness due to the extrapolation. In the experiments, we compare ERTR with state-of-the-art tree algorithms on real datasets to show the superior performance of our model. Moreover, promising improvements are brought by using the extrapolated trees as base learners in the extension of ERTR to ensemble methods.

The success of self-supervised learning in computer vision and natural language processing has motivated pretraining methods on tabular data. However, most existing tabular self-supervised learning models fail to leverage information across multiple data tables and cannot generalize to new tables. In this work, we introduce XTab, a framework for cross-table pretraining of tabular transformers on datasets from various domains. We address the challenge of inconsistent column types and quantities among tables by utilizing independent featurizers and using federated learning to pretrain the shared component. Tested on 84 tabular prediction tasks from the OpenML-AutoML Benchmark (AMLB), we show that (1) XTab consistently boosts the generalizability, learning speed, and performance of multiple tabular transformers, (2) by pretraining FT-Transformer via XTab, we achieve superior performance than other state-of-the-art tabular deep learning models on various tasks such as regression, binary, and multiclass classification.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

We initiate the study of strategic behavior in screening processes with multiple classifiers. We focus on two contrasting settings: a "conjunctive'' setting in which an individual must satisfy all classifiers simultaneously, and a sequential setting in which an individual to succeed must satisfy classifiers one at a time. In other words, we introduce the combination of strategic classificationwith screening processes. We show that sequential screening pipelines exhibit new and surprising behavior where individuals can exploit the sequential ordering of the tests to "zig-zag'' between classifiers without having to simultaneously satisfy all of them. We demonstrate an individual can obtain a positive outcome using a limited manipulation budget even when far from the intersection of the positive regions of every classifier. Finally, we consider a learner whose goal is to design a sequential screening process that is robust to such manipulations, and provide a construction for the learner that optimizes a natural objective.

Predictive black-box models can exhibit high-accuracy but their opaque nature hinders their uptake in safety-critical deployment environments. Explanation methods (XAI) can provide confidence for decision-making through increased transparency. However, existing XAI methods are not tailored towards models in sensitive domains where one predictor is of special interest, such as a treatment effect in a clinical model, or ethnicity in policy models. We introduce Path-Wise Shapley effects (PWSHAP), a framework for assessing the targeted effect of a binary (e.g. treatment) variable from a complex outcome model. Our approach augments the predictive model with a user-defined directed acyclic graph (DAG). The method then uses the graph alongside on-manifold Shapley values to identify effects along causal pathways whilst maintaining robustness to adversarial attacks. We establish error bounds for the identified path-wise Shapley effects and for Shapley values. We show PWSHAP can perform local bias and mediation analyses with faithfulness to the model. Further, if the targeted variable is randomised we can quantify local effect modification. We demonstrate the resolution, interpretability and true locality of our approach on examples and a real-world experiment.

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) $G^*$ while minimizing the number of interventions made. In our setting, we are additionally given side information about $G^*$ as advice, e.g. a DAG $G$ purported to be $G^*$. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on _algorithms with predictions_. When the advice is a DAG $G$, we design an adaptive search algorithm to recover $G^*$ whose intervention cost is at most $\mathcal{O}(\max\{1, \log \psi\})$ times the cost for verifying $G^*$; here, $\psi$ is a distance measure between $G$ and $G^*$ that is upper bounded by the number of variables $n$, and is exactly 0 when $G=G^*$. Our approximation factor matches the state-of-the-art for the advice-less setting.

Given a sequence of observable variables $\{(x_1, y_1), \ldots, (x_n, y_n)\}$, the conformal prediction method estimates a confidence set for $y_{n+1}$ given $x_{n+1}$ that is valid for any finite sample size by merely assuming that the joint distribution of the data is permutation invariant. Although attractive, computing such a set is computationally infeasible in most regression problems. Indeed, in these cases, the unknown variable $y_{n+1}$ can take an infinite number of possible candidate values, and generating conformal sets requires retraining a predictive model for each candidate. In this paper, we focus on a sparse linear model with only a subset of variables for prediction and use numerical continuation techniques to approximate the solution path efficiently. The critical property we exploit is that the set of selected variables is invariant under a small perturbation of the input data. Therefore, it is sufficient to enumerate and refit the model only at the change points of the set of active features and smoothly interpolate the rest of the solution via a Predictor-Corrector mechanism. We show how our path-following algorithm accurately approximates conformal prediction sets and illustrate its performance using synthetic and real data examples.

Natural intelligences (NIs) thrive in a dynamic world - they learn quickly, sometimes with only a few samples. In contrast, artificial intelligences (AIs) typically learn with a prohibitive number of training samples and computational power. What design principle difference between NI and AI could contribute to such a discrepancy? Here, we investigate the role of weight polarity: development processes initialize NIs with advantageous polarity configurations; as NIs grow and learn, synapse magnitudes update, yet polarities are largely kept unchanged. We demonstrate with simulation and image classification tasks that if weight polarities are **adequately** set ***a priori***, then networks learn with less time and data. We also explicitly illustrate situations in which *a priori* setting the weight polarities is disadvantageous for networks. Our work illustrates the value of weight polarities from the perspective of statistical and computational efficiency during learning.

We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar property $\Gamma$ if and only if $\Gamma$ is *elicitable*. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable $\Gamma$, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a $\Gamma$-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property $\Gamma^1$ is not elicitable by itself, but *is* elicitable *conditionally* on another elicitable property $\Gamma^0$, then there is a canonical algorithm that *jointly* multicalibrates $\Gamma^1$ and $\Gamma^0$; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.