We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine learning and signal processing literature, under the names of concept drift, stochastic tracking, and performative prediction. We provide novel non-asymptotic convergence guarantees for stochastic algorithms with iterate averaging, focusing on bounds valid both in expectation and with high probability. The efficiency estimates we obtain clearly decouple the contributions of optimization error, gradient noise, and time drift. Notably, we identify a low drift-to-noise regime in which the tracking efficiency of the proximal stochastic gradient method benefits significantly from a step decay schedule. Numerical experiments illustrate our results.
We consider the hypothesis that Evolution promotes population-wide genome patterns that, under randomization, ensures the External Validity of adaptations across population members. An adaptation is Externally Valid (EV) if its effect holds under a wide range of population genetic variations. A prediction following the hypothesis is that pairwise base substitutions in segregating regions must be 'random' as in Erdos-Renyi-Gilbert random graphs, but with edge probabilities derived from Experimental-Design concepts. We demonstrate these probabilities, and consequent mutation rates, in the full-genomes of 2504 humans, 1135 flowering plants, 1170 flies, 453 domestic sheep and 1223 brown rats.
Unobserved confounding is a fundamental obstacle to establishing valid causal conclusions from observational data. Two complementary types of approaches have been developed to address this obstacle: obtaining identification using fortuitous external aids, such as instrumental variables or proxies, or by means of the ID algorithm, using Markov restrictions on the full data distribution encoded in graphical causal models. In this paper we aim to develop a synthesis of the former and latter approaches to identification in causal inference to yield the most general identification algorithm in multivariate systems currently known -- the proximal ID algorithm. In addition to being able to obtain nonparametric identification in all cases where the ID algorithm succeeds, our approach allows us to systematically exploit proxies to adjust for the presence of unobserved confounders that would have otherwise prevented identification. In addition, we outline a class of estimation strategies for causal parameters identified by our method in an important special case. We illustrate our approach by simulation studies and a data application.
Data-driven learning algorithms are employed in many online applications, in which data become available over time, like network monitoring, stock price prediction, job applications, etc. The underlying data distribution might evolve over time calling for model adaptation as new instances arrive and old instances become obsolete. In such dynamic environments, the so-called data streams, fairness-aware learning cannot be considered as a one-off requirement, but rather it should comprise a continual requirement over the stream. Recent fairness-aware stream classifiers ignore the problem of class imbalance, which manifests in many real-life applications, and mitigate discrimination mainly because they "reject" minority instances at large due to their inability to effectively learn all classes. In this work, we propose \ours, an online fairness-aware approach that maintains a valid and fair classifier over the stream. \ours~is an online boosting approach that changes the training distribution in an online fashion by monitoring stream's class imbalance and tweaks its decision boundary to mitigate discriminatory outcomes over the stream. Experiments on 8 real-world and 1 synthetic datasets from different domains with varying class imbalance demonstrate the superiority of our method over state-of-the-art fairness-aware stream approaches with a range (relative) increase [11.2\%-14.2\%] in balanced accuracy, [22.6\%-31.8\%] in gmean, [42.5\%-49.6\%] in recall, [14.3\%-25.7\%] in kappa and [89.4\%-96.6\%] in statistical parity (fairness).
The recently developed pure Transformer architectures have attained promising accuracy on point cloud learning benchmarks compared to convolutional neural networks. However, existing point cloud Transformers are computationally expensive since they waste a significant amount of time on structuring the irregular data. To solve this shortcoming, we present Sparse Window Attention (SWA) module to gather coarse-grained local features from non-empty voxels, which not only bypasses the expensive irregular data structuring and invalid empty voxel computation, but also obtains linear computational complexity with respect to voxel resolution. Meanwhile, to gather fine-grained features about the global shape, we introduce relative attention (RA) module, a more robust self-attention variant for rigid transformations of objects. Equipped with the SWA and RA, we construct our neural architecture called PVT that integrates both modules into a joint framework for point cloud learning. Compared with previous Transformer-based and attention-based models, our method attains top accuracy of 94.0% on classification benchmark and 10x inference speedup on average. Extensive experiments also valid the effectiveness of PVT on part and semantic segmentation benchmarks (86.6% and 69.2% mIoU, respectively).
This work addresses the challenging task of LiDAR-based 3D object detection in foggy weather. Collecting and annotating data in such a scenario is very time, labor and cost intensive. In this paper, we tackle this problem by simulating physically accurate fog into clear-weather scenes, so that the abundant existing real datasets captured in clear weather can be repurposed for our task. Our contributions are twofold: 1) We develop a physically valid fog simulation method that is applicable to any LiDAR dataset. This unleashes the acquisition of large-scale foggy training data at no extra cost. These partially synthetic data can be used to improve the robustness of several perception methods, such as 3D object detection and tracking or simultaneous localization and mapping, on real foggy data. 2) Through extensive experiments with several state-of-the-art detection approaches, we show that our fog simulation can be leveraged to significantly improve the performance for 3D object detection in the presence of fog. Thus, we are the first to provide strong 3D object detection baselines on the Seeing Through Fog dataset. Our code is available at www.trace.ethz.ch/lidar_fog_simulation.
Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The defeasible logic $DL(\partial_{||})$ was introduced as a more scalable alternative to $DL(\partial)$, which is better known. In this paper we consider the use of (implementations of) $DL(\partial_{||})$ as a computational aid to computing conclusions in $DL(\partial)$ and other defeasible logics, rather than as an alternative to $DL(\partial)$. We identify conditions under which $DL(\partial_{||})$ can be substituted for $DL(\partial)$ with no change to the conclusions drawn, and conditions under which $DL(\partial_{||})$ can be used to draw some valid conclusions, leaving the remainder to be drawn by $DL(\partial)$.
Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in the meantime a few invalid ones may undermine consistency. This paper investigates the empirical likelihood estimation of these moment-defined models in high-dimensional settings. We propose a penalized empirical likelihood (PEL) estimation and establish its oracle property with consistent detection of invalid moments. The PEL estimator is asymptotically normally distributed, and a projected PEL procedure further eliminates its asymptotic bias and provides more accurate normal approximation to the finite sample behavior. Simulation exercises demonstrate excellent numerical performance of these methods in estimation and inference.
We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models. We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples. Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences. We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.
Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of portfolios. In practical settings, the optimal choice may be much larger than the standard choices of 5 or 10. To illustrate the relevance of our results, we revisit the size and momentum anomalies.
Modern empirical work in Regression Discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show they yield suboptimal confidence intervals in terms of coverage error. We establish valid coverage error expansions for RBC confidence interval estimators and use these results to propose new inference-optimal bandwidth choices for forming these intervals. We find that the standard MSE-optimal bandwidth for the RD point estimator is too large when the goal is to construct RBC confidence intervals with the smallest coverage error. We further optimize the constant terms behind the coverage error to derive new optimal choices for the auxiliary bandwidth required for RBC inference. Our expansions also establish that RBC inference yields higher-order refinements (relative to traditional undersmoothing) in the context of RD designs. Our main results cover sharp and sharp kink RD designs under conditional heteroskedasticity, and we discuss extensions to fuzzy and other RD designs, clustered sampling, and pre-intervention covariates adjustments. The theoretical findings are illustrated with a Monte Carlo experiment and an empirical application, and the main methodological results are available in \texttt{R} and \texttt{Stata} packages.
Mistakes in machine learning practice are commonplace, and can result in a loss of confidence in the findings and products of machine learning. This guide outlines common mistakes that occur when using machine learning, and what can be done to avoid them. Whilst it should be accessible to anyone with a basic understanding of machine learning techniques, it focuses on issues that are of particular concern within academic research, such as the need to do rigorous comparisons and reach valid conclusions. It covers five stages of the machine learning process: what to do before model building, how to reliably build models, how to robustly evaluate models, how to compare models fairly, and how to report results.
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of well-localized functional parts with specific geometric features. Often, these features are strongly correlated -- a modification of facial traits in a quadruped should induce changes to the body structure. However, in shape modelling applications, these types of edits are among the hardest ones; they require high precision, but also a global awareness of the entire shape. Even in the deep learning era, obtaining manipulable representations that satisfy such requirements is an open problem posing significant constraints. In this work, we address this problem by defining a data-driven model upon a family of linear operators (variants of the mesh Laplacian), whose spectra capture global and local geometric properties of the shape at hand. Modifications to these spectra are translated to semantically valid deformations of the corresponding surface. By explicitly decoupling the global from the local surface features, our pipeline allows to perform local edits while simultaneously maintaining a global stylistic coherence. We empirically demonstrate how our learning-based model generalizes to shape representations not seen at training time, and we systematically analyze different choices of local operators over diverse shape categories.
We develop a Stata command, bootranktest, for implementing the matrix rank test of Chen and Fang (2019) in linear instrumental variable regression models. Existing rank tests employ critical values that may be too small, and hence may not even be first order valid in the sense that they may fail to control the Type I error. By appealing to the bootstrap, they devise a test that overcomes the deficiency of existing tests. The command bootranktest implements the two-step version of their test, and also the analytic version if chosen. The command also accommodates data with temporal and cluster dependence.
This paper considers identification and inference for the distribution of treatment effects conditional on observable covariates. Since the conditional distribution of treatment effects is not point identified without strong assumptions, we obtain bounds on the conditional distribution of treatment effects by using the Makarov bounds. We also consider the case where the treatment is endogenous and propose two stochastic dominance assumptions to tighten the bounds. We develop a nonparametric framework to estimate the bounds and establish the asymptotic theory that is uniformly valid over the support of treatment effects. An empirical example illustrates the usefulness of the methods.
Randomized Smoothing (RS), being one of few provable defenses, has been showing great effectiveness and scalability in terms of defending against $\ell_2$-norm adversarial perturbations. However, the cost of MC sampling needed in RS for evaluation is high and computationally expensive. To address this issue, we investigate the possibility of performing randomized smoothing and establishing the robust certification in the latent space of a network, so that the overall dimensionality of tensors involved in computation could be drastically reduced. To this end, we propose Latent Space Randomized Smoothing. Another important aspect is that we use orthogonal modules, whose Lipschitz property is known for free by design, to propagate the certified radius estimated in the latent space back to the input space, providing valid certifiable regions for the test samples in the input space. Experiments on CIFAR10 and ImageNet show that our method achieves competitive certified robustness but with a significant improvement of efficiency during the test phase.
Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad-hoc without a clear physical explanation. We investigated data-driven models theoretically on a linear system. We argue that these models are equivalent to non-linear length scale scaling laws of transport coefficients. The equivalence to scaling laws justified the physical plausibility and revealed the limitation of data-driven models. Our argument also points out that modeling the scaling law could avoid practical difficulties in data-driven models like derivative estimation and variable selection on noisy data. We further proposed a constitutive relation model based on scaling law and tested it on the calculation of Rayleigh scattering spectra. The result shows our data-driven model has a clear advantage over the Chapman-Enskog expansion and moment methods.
This paper investigates the assumption of homogeneous effects of federal tax changes across the U.S. states and identifies where and why that assumption may not be valid. More specifically, what determines the transmission mechanism of tax shocks at the state level? How vital are states' fiscal structures, financial conditions, labor market rigidities, and industry mix? Do these economic and structural characteristics drive the transmission mechanism of the tax changes at the state level at different horizons? This study employs a panel factor-augmented vector autoregression (FAVAR) technique to answer these issues. The findings show that state economies respond homogeneously in terms of employment and price levels; however, they react heterogeneously in real GDP and personal income growth. In most states, these reactions are statistically significant, and the heterogeneity in the effects of tax cuts is significantly related to the state's fiscal structure, manufacturing and financial composition, and the labor market's rigidity. A cross-state regression analysis shows that states with higher tax elasticity, higher personal income tax, strict labor market regulation, and economic policy uncertainties are relatively less responsive to federal tax changes. In contrast, the magnitude of the response in real GDP, personal income, and employment to tax cuts is relatively higher in states with a larger share of finance, manufacturing, lower tax burdens, and flexible credit markets.
Recently, transfer subspace learning based approaches have shown to be a valid alternative to unsupervised subspace clustering and temporal data clustering for human motion segmentation (HMS). These approaches leverage prior knowledge from a source domain to improve clustering performance on a target domain, and currently they represent the state of the art in HMS. Bucking this trend, in this paper, we propose a novel unsupervised model that learns a representation of the data and digs clustering information from the data itself. Our model is reminiscent of temporal subspace clustering, but presents two critical differences. First, we learn an auxiliary data matrix that can deviate from the initial data, hence confer more degrees of freedom to the coding matrix. Second, we introduce a regularization term for this auxiliary data matrix that preserves the local geometrical structure present in the high-dimensional space. The proposed model is efficiently optimized by using an original Alternating Direction Method of Multipliers (ADMM) formulation allowing to learn jointly the auxiliary data representation, a nonnegative dictionary and a coding matrix. Experimental results on four benchmark datasets for HMS demonstrate that our approach achieves significantly better clustering performance then state-of-the-art methods, including both unsupervised and more recent semi-supervised transfer learning approaches.
Many available formal verification methods have been shown to be instances of a unified Branch-and-Bound (BaB) formulation. We propose a novel machine learning framework that can be used for designing an effective branching strategy as well as for computing better lower bounds. Specifically, we learn two graph neural networks (GNN) that both directly treat the network we want to verify as a graph input and perform forward-backward passes through the GNN layers. We use one GNN to simulate the strong branching heuristic behaviour and another to compute a feasible dual solution of the convex relaxation, thereby providing a valid lower bound. We provide a new verification dataset that is more challenging than those used in the literature, thereby providing an effective alternative for testing algorithmic improvements for verification. Whilst using just one of the GNNs leads to a reduction in verification time, we get optimal performance when combining the two GNN approaches. Our combined framework achieves a 50\% reduction in both the number of branches and the time required for verification on various convolutional networks when compared to several state-of-the-art verification methods. In addition, we show that our GNN models generalize well to harder properties on larger unseen networks.