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This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile contours and regions and closed-form formulas under the classical assumption of rotational symmetry. The empirical versions of our distribution functions enjoy the expected Glivenko-Cantelli property of traditional distribution functions. They provide fully distribution-free concepts of ranks and signs and define data-driven systems of (curvilinear) parallels and (hyper)meridians. Based on this, we also construct a universally consistent test of uniformity and a class of fully distribution-free and universally consistent tests for directional MANOVA which, in simulations, outperform all their existing competitors. A real-data example involving the analysis of sunspots concludes the paper.

Monitoring concurrent programs typically rely on collecting traces to abstract program executions. However, existing approaches targeting general behavioral properties are either not tailored for online monitoring, are no longer maintained, or implement naive instrumentation that often leads to unsound verdicts. We first define the notion of when a trace is representative of a concurrent execution. We then present a non-blocking vector clock algorithm to collect sound concurrent traces on the fly reflecting the partial order between events. Moreover, concurrent events in the representative trace pose a soundness problem for monitors synthesized from total order formalisms. For this, we extract a causal dependence relation from the monitor to check if the trace has the needed orderings and define the conditions to decide at runtime when a collected trace is monitorable. We implement our contributions in a tool, FACTS, which instruments programs compiling to Java bytecode, constructs sound representative traces, and warns the monitor about non-monitorable traces. We evaluate our work and compare it with existing approaches.

This paper tackles the challenge of teaching code semantics to Large Language Models (LLMs) for program analysis by incorporating code symmetries into the model architecture. We introduce a group-theoretic framework that defines code symmetries as semantics-preserving transformations, where forming a code symmetry group enables precise and efficient reasoning of code semantics. Our solution, SymC, develops a novel variant of self-attention that is provably equivariant to code symmetries from the permutation group defined over the program dependence graph. SymC obtains superior performance on five program analysis tasks, outperforming state-of-the-art code models, including GPT-4, without any pre-training. Our results suggest that code LLMs that encode the code structural prior via the code symmetry group generalize better and faster.

Machine learning methods for estimating heterogeneous treatment effects (HTE) facilitate large-scale personalized decision-making across various domains such as healthcare, policy making, education, and more. Current machine learning approaches for HTE require access to substantial amounts of data per treatment, and the high costs associated with interventions makes centrally collecting so much data for each intervention a formidable challenge. To overcome this obstacle, in this work, we propose a novel framework for collaborative learning of HTE estimators across institutions via Federated Learning. We show that even under a diversity of interventions and subject populations across clients, one can jointly learn a common feature representation, while concurrently and privately learning the specific predictive functions for outcomes under distinct interventions across institutions. Our framework and the associated algorithm are based on this insight, and leverage tabular transformers to map multiple input data to feature representations which are then used for outcome prediction via multi-task learning. We also propose a novel way of federated training of personalised transformers that can work with heterogeneous input feature spaces. Experimental results on real-world clinical trial data demonstrate the effectiveness of our method.

We propose a new method for cloth digitalization. Deviating from existing methods which learn from data captured under relatively casual settings, we propose to learn from data captured in strictly tested measuring protocols, and find plausible physical parameters of the cloths. However, such data is currently absent, so we first propose a new dataset with accurate cloth measurements. Further, the data size is considerably smaller than the ones in current deep learning, due to the nature of the data capture process. To learn from small data, we propose a new Bayesian differentiable cloth model to estimate the complex material heterogeneity of real cloths. It can provide highly accurate digitalization from very limited data samples. Through exhaustive evaluation and comparison, we show our method is accurate in cloth digitalization, efficient in learning from limited data samples, and general in capturing material variations. Code and data are available //github.com/realcrane/Bayesian-Differentiable-Physics-for-Cloth-Digitalization

Variational flows allow practitioners to learn complex continuous distributions, but approximating discrete distributions remains a challenge. Current methodologies typically embed the discrete target in a continuous space - usually via continuous relaxation or dequantization - and then apply a continuous flow. These approaches involve a surrogate target that may not capture the original discrete target, might have biased or unstable gradients, and can create a difficult optimization problem. In this work, we develop a variational flow family for discrete distributions without any continuous embedding. First, we develop a measure-preserving and discrete (MAD) invertible map that leaves the discrete target invariant, and then create a mixed variational flow (MAD Mix) based on that map. Our family provides access to i.i.d. sampling and density evaluation with virtually no tuning effort. We also develop an extension to MAD Mix that handles joint discrete and continuous models. Our experiments suggest that MAD Mix produces more reliable approximations than continuous-embedding flows while being significantly faster to train.

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of two independent processes: one spanned by a finite basis of inducing points and the other capturing the remaining variation. We show that this formulation recovers existing approximations and at the same time allows to obtain tighter lower bounds on the marginal likelihood and new stochastic variational inference algorithms. We demonstrate the efficiency of these algorithms in several Gaussian process models ranging from standard regression to multi-class classification using (deep) convolutional Gaussian processes and report state-of-the-art results on CIFAR-10 among purely GP-based models.

Weak coin flipping is an important cryptographic primitive -- it is the strongest known secure two-party computation primitive that classically becomes secure only under certain assumptions (e.g. computational hardness), while quantumly there exist protocols that achieve arbitrarily close to perfect security. This breakthrough result was established by Mochon in 2007 [arXiv:0711.4114]. However, his proof relied on the existence of certain unitary operators which was established by a non-constructive argument. Consequently, explicit protocols have remained elusive. In this work, we give exact constructions of related unitary operators. These, together with a new formalism, yield a family of protocols approaching perfect security thereby also simplifying Mochon's proof of existence. We illustrate the construction of explicit weak coin flipping protocols by considering concrete examples (from the aforementioned family of protocols) that are more secure than all previously known protocols.

We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true regression function lies in an $L_2$-fractional Sobolev space with order $s\in (0,1)$. This function class is a Hilbert space lying between the space of square-integrable functions and the first-order Sobolev space consisting of differentiable functions. It contains fractional power functions, piecewise constant or polynomial functions and bump function as canonical examples. For the proposed approach, we prove upper bounds on the in-sample mean-squared estimation error of order $n^{-\frac{2s}{2s+d}}$, where $d$ is the dimension, $s$ is the aforementioned order parameter and $n$ is the number of observations. We also provide preliminary empirical results validating the practical performance of the developed estimators.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.