AISTATS 2024 论文列表

In-context learning (ICL) is a new paradigm for natural language processing that utilizes Generative Pre-trained Transformer (GPT)-like models. This approach uses prompts that include in-context demonstrations to generate the corresponding output for a new query input. However, applying ICL in real cases does not scale with the number of samples, and lacks robustness to different prompt templates and demonstration permutations. In this paper, we first show that GPT-like models using ICL result in unreliable predictions based on a new metric based on Shannon entropy. Then, to solve this problem, we propose a new technique called the Linear Probe Calibration (LinC), a method that calibrates the model’s output probabilities, resulting in reliable predictions and improved performance, while requiring only minimal additional samples (as few as five labeled data samples). LinC significantly enhances the ICL test performance of GPT models on various benchmark datasets, with an average improvement of up to 21%, and up to a 50% improvement in some cases, and significantly boosts the performance of PEFT methods, especially in the low resource regime. Moreover, LinC achieves lower expected calibration error, and is highly robust to varying label proportions, prompt templates, and demonstration permutations.

Bilevel optimization aims to optimize an outer objective function that depends on the solution to an inner optimization problem. It is routinely used in Machine Learning, notably for hyperparameter tuning. The conventional method to compute the so-called hypergradient of the outer problem is to use the Implicit Function Theorem (IFT). As a function of the error of the inner problem resolution, we study the error of the IFT method. We analyze two strategies to reduce this error: preconditioning the IFT formula and reparameterizing the inner problem. We give a detailed account of the impact of these two modifications on the error, highlighting the role played by higher-order derivatives of the functionals at stake. Our theoretical findings explain when super efficiency, namely reaching an error on the hypergradient that depends quadratically on the error on the inner problem, is achievable and compare the two approaches when this is impossible. Numerical evaluations on hyperparameter tuning for regression problems substantiate our theoretical findings.

Enhancing the stability of machine learning algorithms under distributional shifts is at the heart of the Out-of-Distribution (OOD) Generalization problem. Derived from causal learning, recent works of invariant learning pursue strict invariance with multiple training environments. Although intuitively reasonable, strong assumptions on the availability and quality of environments are made to learn the strict invariance property. In this work, we come up with the “distributional stability" notion to mitigate such limitations. It quantifies the stability of prediction mechanisms among sub-populations down to a prescribed scale. Based on this, we propose the learnability assumption and derive the generalization error bound under distribution shifts. Inspired by theoretical analyses, we propose our novel stable risk minimization (SRM) algorithm to enhance the model’s stability w.r.t. shifts in prediction mechanisms (Y|X-shifts). Experimental results are consistent with our intuition and validate the effectiveness of our algorithm. The code can be found at https://github.com/LJSthu/SRM.

We propose a new optimization-based approach for feature selection in tree ensembles, an important problem in statistics and machine learning. Popular tree ensemble toolkits e.g., Gradient Boosted Trees and Random Forests support feature selection post-training based on feature importance scores, while very popular, they are known to have drawbacks. We propose Skinny Trees: an end-to-end toolkit for feature selection in tree ensembles where we train a tree ensemble while controlling the number of selected features. Our optimization-based approach learns an ensemble of differentiable trees, and simultaneously performs feature selection using a grouped $\ell_0$-regularizer. We use first-order methods for optimization and present convergence guarantees for our approach. We use a dense-to-sparse regularization scheduling scheme that can lead to more expressive and sparser tree ensembles. On 15 synthetic and real-world datasets, Skinny Trees can achieve $1.5{\times}$–$620{\times}$ feature compression rates, leading up to $10{\times}$ faster inference over dense trees, without any loss in performance. Skinny Trees lead to superior feature selection than many existing toolkits e.g., in terms of AUC performance for 25% feature budget, Skinny Trees outperforms LightGBM by 10.2% (up to 37.7%), and Random Forests by 3% (up to 12.5%).

Numerous online services are data-driven: the behavior of users affects the system’s parameters, and the system’s parameters affect the users’ experience of the service, which in turn affects the way users may interact with the system. For example, people may choose to use a service only for tasks that already works well, or they may choose to switch to a different service. These adaptations influence the ability of a system to learn about a population of users and tasks in order to improve its performance broadly. In this work, we analyze a class of such dynamics—where users allocate their participation amongst services to reduce the individual risk they experience, and services update their model parameters to reduce the service’s risk on their current user population. We refer to these dynamics as \emph{risk-reducing}, which cover a broad class of common model updates including gradient descent and multiplicative weights. For this general class of dynamics, we show that asymptotically stable equilibria are always segmented, with sub-populations allocated to a single learner. Under mild assumptions, the utilitarian social optimum is a stable equilibrium. In contrast to previous work, which shows that repeated risk minimization can result in representation disparity and high overall loss with a single learner (Hashimoto et al., 2018; Miller et al., 2021), we find that repeated myopic updates with multiple learners lead to better outcomes. We illustrate the phenomena via a simulated example initialized from real data.

Randomized controlled trials (RCTs) are gold standards for assessing intervention efficacy. Yet, generalizing evidence from classical RCTs can be challenging and sometimes problematic due to their limited external validity under stringent eligibility criteria and inadequate statistical power resulting from limited sample sizes under budgetary constraints. "Digital clinical trial," which utilizes digital technology and electronic medical records (EMRs) to expand eligibility criteria and enhance data collection efficiency, offers a promising concept for solving the above-mentioned conundrums encountered in classical RCTs. In this paper, we propose two novel digital clinical trial design strategies assisted by EMRs collected from diverse patient populations. On the one hand, leveraging digital technologies, our design strategies adaptively modify both the eligibility criteria and treatment assignment mechanism to enhance data collection efficiency. As a result, evidence gathered from our design can possess greater statistical power. On the other hand, since EMRs capture diverse patient populations and provide large sample sizes, our design not only broadens the trial’s eligibility criteria but also enhances its statistical power, enabling us to collect more generalizable evidence with boosted statistical power for evaluating intervention efficacy than classical RCTs. We demonstrate the validity and merit of the proposed designs with detailed theoretical investigation, simulation studies, and a synthetic case study.

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this purpose. In many technical applications the design space is explored via continuous trajectories, along which the safety needs to be assessed. This is particularly challenging for strict safety requirements in GP methods, as it employs computationally expensive Monte Carlo sampling of high quantiles. We address these challenges by providing provable safety bounds based on the adaptively sampled median of the supremum of the posterior GP. Our method significantly reduces the number of samples required for estimating high safety probabilities, resulting in faster evaluation without sacrificing accuracy and exploration speed. The effectiveness of our safe active learning approach is demonstrated through extensive simulations and validated using a real-world engine example.

We develop a family of fast variational methods for sequential control in dynamic settings where an agent is incentivized to maximize information gain. We consider the case of optimal control in continuous nonlinear dynamical systems that prohibit exact evaluation of the mutual information (MI) reward. Our approach couples efficient message-passing inference with variational bounds on the MI objective under Gaussian projections. We also develop a Gaussian mixture approximation that enables exact MI evaluation under constraints on the component covariances. We validate our methodology in nonlinear systems with superior and faster control compared to standard particle-based methods. We show our approach improves the accuracy and efficiency of one-shot robotic learning with intrinsic MI rewards. Furthermore, we demonstrate that our method is applicable to a wider range of contexts, e.g., the active information acquisition problem.

We consider the problem of efficiently routing jobs that arrive into a central queue to a system of heterogeneous servers. Unlike homogeneous systems, a threshold policy, that routes jobs to the slow server(s) when the queue length exceeds a certain threshold, is known to be optimal for the one-fast-one-slow two-server system. But an optimal policy for the multi-server system is unknown and non-trivial to find. While Reinforcement Learning (RL) has been recognized to have great potential for learning policies in such cases, our problem has an exponentially large state space size, rendering standard RL inefficient. In this work, we propose ACHQ, an efficient policy gradient based algorithm with a low dimensional soft threshold policy parameterization that leverages the underlying queueing structure. We provide stationary-point convergence guarantees for the general case and despite the low-dimensional parameterization prove that ACHQ converges to an approximate global optimum for the special case of two servers. Simulations demonstrate an improvement in expected response time of up to ${\sim}30%$ over the greedy policy that routes to the fastest available server.

The agnostic setting is the hardest generalization of the PAC model since it is akin to learning with adversarial noise. In this paper, we give a poly $(n, t, 1/\epsilon)$ quantum algorithm for learning size $t$ decision trees over $n$-bit inputs with uniform marginal over instances, in the agnostic setting, without membership queries (MQ). This is the first algorithm (classical or quantum) for efficiently learning decision trees without MQ. First, we construct a quantum agnostic weak learner by designing a quantum variant of the classical Goldreich-Levin algorithm that works with strongly biased function oracles. Next, we show how to quantize the agnostic boosting algorithm by Kalai and Kanade (2009) to obtain the first efficient quantum agnostic boosting algorithm (that has a polynomial speedup over existing adaptive quantum boosting algorithms). We then use the quantum agnostic boosting algorithm to boost the weak quantum agnostic learner constructed previously to obtain a quantum agnostic learner for decision trees. Using the above framework, we also give quantum decision tree learning algorithms without MQ in weaker noise models.

The relationship between architecture and performance is critical for improving the efficiency of neural architecture design, yet few efforts have been devoted to understanding this relationship between architecture and performance, especially architecture-performance joint distribution. In this paper, we propose Semi-Supervised Generative Adversarial Networks Neural Architecture Design Method or SemiGAN-NAD to capture the architecture-performance joint distribution with few performance labels. It is composed of Bidirectional Transformer of Architecture and Performance (Bi-Arch2Perf) and Neural Architecture Conditional Generation (NACG). Bi-Arch2Perf is developed to learn the joint distribution of architecture and performance from bidirectional conditional distribution through the adversarial training of the discriminator, the architecture generator, and the performance predictor. Then, the incorporation of semi-supervised learning optimizes the construction of Bi-Arch2Perf by utilizing a large amount of architecture information without performance annotation in search space. Based on the learned bidirectional relationship, the performance of architecture is predicted by NACG in high-performance architecture space to efficiently discover well-promising neural architectures. The experimental results on NAS benchmarks demonstrate that SemiGAN-NAD achieves competitive performance with reduced evaluation time compared with the latest NAS methods. Moreover, the high-performance architecture signatures learned by Bi-Arch2Perf are also illustrated in our experiments.

Many machine learning tasks can be solved by minimizing a convex function of an occupancy measure over the policies that generate them. These include reinforcement learning, imitation learning, among others. This more general paradigm is called the Concave Utility Reinforcement Learning problem (CURL). Since CURL invalidates classical Bellman equations, it requires new algorithms. We introduce MD-CURL, a new algorithm for CURL in a finite horizon Markov decision process. MD-CURL is inspired by mirror descent and uses a non-standard regularization to achieve convergence guarantees and a simple closed-form solution, eliminating the need for computationally expensive projection steps typically found in mirror descent approaches. We then extend CURL to an online learning scenario and present Greedy MD-CURL, a new method adapting MD-CURL to an online, episode-based setting with partially unknown dynamics. Like MD-CURL, the online version Greedy MD-CURL benefits from low computational complexity, while guaranteeing sub-linear or even logarithmic regret, depending on the level of information available on the underlying dynamics.

In this work, we present a novel approach for compressing overparameterized models, developed through studying their learning dynamics. We observe that for many deep models, updates to the weight matrices occur within a low-dimensional invariant subspace. For deep linear models, we demonstrate that their principal components are fitted incrementally within a small subspace, and use these insights to propose a compression algorithm for deep linear networks that involve decreasing the width of their intermediate layers. We empirically evaluate the effectiveness of our compression technique on matrix recovery problems. Remarkably, by using an initialization that exploits the structure of the problem, we observe that our compressed network converges faster than the original network, consistently yielding smaller recovery errors. We substantiate this observation by developing a theory focused on deep matrix factorization. Finally, we empirically demonstrate how our compressed model has the potential to improve the utility of deep nonlinear models. Overall, our algorithm improves the training efficiency by more than 2x, without compromising generalization.

The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood estimation (MLE) of the precision matrix, subject to Laplacian structural constraints, with a sparsity-inducing penalty term. This paper aims to solve this learning problem accurately and efficiently. First, since the commonly used $\ell_1$-norm penalty is inappropriate in this setting and may lead to a complete graph, we employ the nonconvex minimax concave penalty (MCP), which promotes sparse solutions with lower estimation bias. Second, as opposed to existing first-order methods for this problem, we develop a second-order proximal Newton approach to obtain an efficient solver, utilizing several algorithmic features, such as using conjugate gradients, preconditioning, and splitting to active/free sets. Numerical experiments demonstrate the advantages of the proposed method in terms of both computational complexity and graph learning accuracy compared to existing methods.

This work aims to address an open problem in data valuation literature concerning the efficient computation of Data Shapley for weighted $K$ nearest neighbor algorithm (WKNN-Shapley). By considering the accuracy of hard-label KNN with discretized weights as the utility function, we reframe the computation of WKNN-Shapley into a counting problem and introduce a quadratic-time algorithm, presenting a notable improvement from $O(N^K)$, the best result from existing literature. We develop a deterministic approximation algorithm that further improves computational efficiency while maintaining the key fairness properties of the Shapley value. Through extensive experiments, we demonstrate WKNN-Shapley’s computational efficiency and its superior performance in discerning data quality compared to its unweighted counterpart.

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 the 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. In this work, we introduce 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.

We study the problem of computationally and label efficient PAC active learning $d$-dimensional halfspaces with Tsybakov Noise (Tsybakov, 2004) under structured unlabeled data distributions. Inspired by Diakonikolas et al., (2020c), we prove that any approximate first-order stationary point of a smooth nonconvex loss function yields a halfspace with a low excess error guarantee. In light of the above structural result, we design a nonconvex optimization-based algorithm with a label complexity of $\tilde{O}(d (\frac{1}{\epsilon})^{\frac{8-6\alpha}{3\alpha-1}})$, under the assumption that the Tsybakov noise parameter $\alpha \in (\frac13, 1]$, which narrows down the gap between the label complexities of the previously known efficient passive or active algorithms (Diakonikolas et al., 2020b; Zhang and Li, 2021) and the information-theoretic lower bound in this setting.

The existence of adversarial attacks on machine learning models imperceptible to a human is still quite a mystery from a theoretical perspective. In this work, we introduce two notions of adversarial attacks: natural or on-manifold attacks, which are perceptible by a human/oracle, and unnatural or off-manifold attacks, which are not. We argue that the existence of the off-manifold attacks is a natural consequence of the dimension gap between the intrinsic and ambient dimensions of the data. For 2-layer ReLU networks, we prove that even though the dimension gap does not affect generalization performance on samples drawn from the observed data space, it makes the clean-trained model more vulnerable to adversarial perturbations in the off-manifold direction of the data space. Our main results provide an explicit relationship between the $\ell_2,\ell_{\infty}$ attack strength of the on/off-manifold attack and the dimension gap.

Modern data-driven and distributed learning frameworks deal with diverse massive data generated by clients spread across heterogeneous environments. Indeed, data heterogeneity is a major bottleneck in scaling up many distributed learning paradigms. In many settings however, heterogeneous data may be generated in clusters with shared structures, as is the case in several applications such as federated learning where a common latent variable governs the distribution of all the samples generated by a client. It is therefore natural to ask how the underlying clustered structures in distributed data can be exploited to improve learning schemes. In this paper, we tackle this question in the special case of estimating $d$-dimensional parameters of a two-component mixture of linear regressions problem where each of $m$ nodes generates $n$ samples with a shared latent variable. We employ the well-known Expectation-Maximization (EM) method to estimate the maximum likelihood parameters from m batches of dependent samples each containing n measurements. Discarding the clustered structure in the mixture model, EM is known to require $O(\log(mn/d))$ iterations to reach the statistical accuracy of $O(\sqrt{d/(mn)}$). In contrast, we show that if initialized properly, EM on the structured data requires only $O(1)$ iterations to reach the same statistical accuracy, as long as m grows up as $e^{o(n)}$. Our analysis establishes and combines novel asymptotic optimization and generalization guarantees for population and empirical EM with dependent samples, which may be of independent interest.