Goldwasser et al.\ (2021) recently proposed the setting of PAC verification, where a hypothesis (machine learning model) that purportedly satisfies the agnostic PAC learning objective is verified using an interactive proof. In this paper we develop this notion further in a number of ways. First, we prove a lower bound for PAC verification of $\Omega(\sqrt{d})$ i.i.d.\ samples for hypothesis classes of VC dimension $d$. Second, we present a protocol for PAC verification of unions of intervals over $\mathbb{R}$ that improves upon their proposed protocol for that task, and matches our lower bound. Third, we introduce a natural generalization of their definition to verification of general statistical algorithms, which is applicable to a wider variety of practical algorithms beyond agnostic PAC learning. Showcasing our proposed definition, our final result is a protocol for the verification of statistical query algorithms that satisfy a combinatorial constraint on their queries.

学习曲线将学习算法的预期误差绘制为标记输入样本数量的函数。它们被机器学习实践者广泛使用，以衡量算法的性能，但是经典的PAC学习理论无法解释其行为。在本文中，我们介绍了一种称为VCL维度的新组合表征，该表征改进并完善了Bousquet等人的最新结果。 （2021）。我们的表征通过提供细粒度的边界来展示学习曲线的结构，并表明对于有限VCL的类，可以将衰减的速率分解为仅取决于假设类别和指数成分的线性组件，该成分是指数的成分。还取决于目标分布。特别是，VCL维度的细微差别意味着比Bousquet等人的边界更强大的下限。 （2021年），比经典的“无免费午餐”下界强。 VCL表征解决了Antos and Lugosi（1998）研究的一个开放问题，他们询问在哪些情况下存在这种下限。作为推论，我们在$ \ mathbb {r}^d $中恢复了其下限，并以原则性的方式也适用于其他情况。最后，为了对我们的工作以及与传统PAC学习界的比较提供另一个观点，我们还以一种更接近PAC环境的语言展示了结果的替代表述。

Accurate determination of a small molecule candidate (ligand) binding pose in its target protein pocket is important for computer-aided drug discovery. Typical rigid-body docking methods ignore the pocket flexibility of protein, while the more accurate pose generation using molecular dynamics is hindered by slow protein dynamics. We develop a tiered tensor transform (3T) algorithm to rapidly generate diverse protein-ligand complex conformations for both pose and affinity estimation in drug screening, requiring neither machine learning training nor lengthy dynamics computation, while maintaining both coarse-grain-like coordinated protein dynamics and atomistic-level details of the complex pocket. The 3T conformation structures we generate are closer to experimental co-crystal structures than those generated by docking software, and more importantly achieve significantly higher accuracy in active ligand classification than traditional ensemble docking using hundreds of experimental protein conformations. 3T structure transformation is decoupled from the system physics, making future usage in other computational scientific domains possible.

Adversarial imitation learning (AIL) has become a popular alternative to supervised imitation learning that reduces the distribution shift suffered by the latter. However, AIL requires effective exploration during an online reinforcement learning phase. In this work, we show that the standard, naive approach to exploration can manifest as a suboptimal local maximum if a policy learned with AIL sufficiently matches the expert distribution without fully learning the desired task. This can be particularly catastrophic for manipulation tasks, where the difference between an expert and a non-expert state-action pair is often subtle. We present Learning from Guided Play (LfGP), a framework in which we leverage expert demonstrations of multiple exploratory, auxiliary tasks in addition to a main task. The addition of these auxiliary tasks forces the agent to explore states and actions that standard AIL may learn to ignore. Additionally, this particular formulation allows for the reusability of expert data between main tasks. Our experimental results in a challenging multitask robotic manipulation domain indicate that LfGP significantly outperforms both AIL and behaviour cloning, while also being more expert sample efficient than these baselines. To explain this performance gap, we provide further analysis of a toy problem that highlights the coupling between a local maximum and poor exploration, and also visualize the differences between the learned models from AIL and LfGP.

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

The Covid-19 pandemic induced a vast increase in adolescents diagnosed with eating disorders and hospitalized due to eating disorders. This immense growth stemmed partially from the stress of the pandemic but also from increased exposure to content that promotes eating disorders via social media, which, within the last decade, has become plagued by pro-eating disorder content. This study aimed to create a deep learning model capable of determining whether a given social media post promotes eating disorders based solely on image data. Tweets from hashtags that have been documented to promote eating disorders along with tweets from unrelated hashtags were collected. After prepossessing, these images were labeled as either pro-eating disorder or not based on which Twitter hashtag they were scraped from. Several deep-learning models were trained on the scraped dataset and were evaluated based on their accuracy, F1 score, precision, and recall. Ultimately, the vision transformer model was determined to be the most accurate, attaining an F1 score of 0.877 and an accuracy of 86.7% on the test set. The model, which was applied to unlabeled Twitter image data scraped from "#selfie", uncovered seasonal fluctuations in the relative abundance of pro-eating disorder content, which reached its peak in the summertime. These fluctuations correspond not only to the seasons, but also to stressors, such as the Covid-19 pandemic. Moreover, the Twitter image data indicated that the relative amount of pro-eating disorder content has been steadily rising over the last five years and is likely to continue increasing in the future.

We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce the problem of exact selective inference to a bivariate truncated Gaussian distribution. By doing so, we give up some power that is achieved with approximate inference in Panigrahi and Taylor (2022). Yet we always produce narrower confidence intervals than a closely related data-splitting procedure. For popular instances of Gaussian regression, this price -- in terms of power -- in exchange for exact selective inference is demonstrated in simulated experiments and in an HIV drug resistance analysis.

Using geometric landmarks like lines and planes can increase navigation accuracy and decrease map storage requirements compared to commonly-used LiDAR point cloud maps. However, landmark-based registration for applications like loop closure detection is challenging because a reliable initial guess is not available. Global landmark matching has been investigated in the literature, but these methods typically use ad hoc representations of 3D line and plane landmarks that are not invariant to large viewpoint changes, resulting in incorrect matches and high registration error. To address this issue, we adopt the affine Grassmannian manifold to represent 3D lines and planes and prove that the distance between two landmarks is invariant to rotation and translation if a shift operation is performed before applying the Grassmannian metric. This invariance property enables the use of our graph-based data association framework for identifying landmark matches that can subsequently be used for registration in the least-squares sense. Evaluated on a challenging landmark matching and registration task using publicly-available LiDAR datasets, our approach yields a 1.7x and 3.5x improvement in successful registrations compared to methods that use viewpoint-dependent centroid and "closest point" representations, respectively.

Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical methods based on discretization are used to solve PDEs. They generally use an estimate of the unknown model parameters and, if available, physical measurements for initialization. Such solvers are often embedded into larger scientific models or analyses with a downstream application such that error quantification plays a key role. However, by entirely ignoring parameter and measurement uncertainty, classical PDE solvers may fail to produce consistent estimates of their inherent approximation error. In this work, we approach this problem in a principled fashion by interpreting solving linear PDEs as physics-informed Gaussian process (GP) regression. Our framework is based on a key generalization of a widely-applied theorem for conditioning GPs on a finite number of direct observations to observations made via an arbitrary bounded linear operator. Crucially, this probabilistic viewpoint allows to (1) quantify the inherent discretization error; (2) propagate uncertainty about the model parameters to the solution; and (3) condition on noisy measurements. Demonstrating the strength of this formulation, we prove that it strictly generalizes methods of weighted residuals, a central class of PDE solvers including collocation, finite volume, pseudospectral, and (generalized) Galerkin methods such as finite element and spectral methods. This class can thus be directly equipped with a structured error estimate and the capability to incorporate uncertain model parameters and observations. In summary, our results enable the seamless integration of mechanistic models as modular building blocks into probabilistic models.

Data deprivation, or the lack of easily available and actionable information on the well-being of individuals, is a significant challenge for the developing world and an impediment to the design and operationalization of policies intended to alleviate poverty. In this paper we explore the suitability of data derived from OpenStreetMap to proxy for the location of two crucial public services: schools and health clinics. Thanks to the efforts of thousands of digital humanitarians, online mapping repositories such as OpenStreetMap contain millions of records on buildings and other structures, delineating both their location and often their use. Unfortunately much of this data is locked in complex, unstructured text rendering it seemingly unsuitable for classifying schools or clinics. We apply a scalable, unsupervised learning method to unlabeled OpenStreetMap building data to extract the location of schools and health clinics in ten countries in Africa. We find the topic modeling approach greatly improves performance versus reliance on structured keys alone. We validate our results by comparing schools and clinics identified by our OSM method versus those identified by the WHO, and describe OSM coverage gaps more broadly.