DeepNLP/NIPS-2020-Accepted-Papers huggingface dataset:
Statistical Guarantees of Distributed Nearest Neighbor Classification
Authors: Jiexin Duan, Xingye Qiao, Guang Cheng

Abstract: Nearest neighbor is a popular nonparametric method for classification and regression with many appealing properties. In the big data era, the sheer volume and spatial/temporal disparity of big data may prohibit centrally processing and storing the data. This has imposed considerable hurdle for nearest neighbor predictions since the entire training data must be memorized. One effective way to overcome this issue is the distributed learning framework. Through majority voting, the distributed nearest neighbor classifier achieves the same rate of convergence as its oracle version in terms of the regret, up to a multiplicative constant that depends solely on the data dimension. The multiplicative difference can be eliminated by replacing majority voting with the weighted voting scheme. In addition, we provide sharp theoretical upper bounds of the number of subsamples in order for the distributed nearest neighbor classifier to reach the optimal convergence rate. It is interesting to note that the weighted voting scheme allows a larger number of subsamples than the majority voting one. Our findings are supported by numerical studies.
Stein Self-Repulsive Dynamics: Benefits From Past Samples
Authors: Mao Ye, Tongzheng Ren, Qiang Liu

Abstract: We propose a new Stein self-repulsive dynamics for obtaining diversified samples from intractable un-normalized distributions. Our idea is to introduce Stein variational gradient as a repulsive force to push the samples of Langevin dynamics away from the past trajectories. This simple idea allows us to significantly decrease the auto-correlation in Langevin dynamics and hence increase the effective sample size. Importantly, as we establish in our theoretical analysis, the asymptotic stationary distribution remains correct even with the addition of the repulsive force, 
thanks to the special properties of the Stein variational gradient. We perform extensive empirical studies of our new algorithm, showing that our method yields much higher sample efficiency and better uncertainty estimation than vanilla Langevin dynamics.
The Statistical Complexity of Early-Stopped Mirror Descent
Authors: Tomas Vaskevicius, Varun Kanade, Patrick Rebeschini

Abstract: Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrained mirror descent algorithms applied to the unregularized empirical risk with the squared loss for linear models and kernel methods. By completing an inequality that characterizes convexity for the squared loss, we identify an intrinsic link between offset Rademacher complexities and potential-based convergence analysis of mirror descent methods. Our observation immediately yields excess risk guarantees for the path traced by the iterates of mirror descent in terms of offset complexities of certain function classes depending only on the choice of the mirror map, initialization point, step-size, and the number of iterations. We apply our theory to recover, in a rather clean and elegant manner via rather short proofs, some of the recent results in the implicit regularization literature, while also showing how to improve upon them in some settings.
Algorithmic recourse under imperfect causal knowledge: a probabilistic approach
Authors: Amir-Hossein Karimi, Julius von Kügelgen, Bernhard Schölkopf, Isabel Valera

Abstract: Recent work has discussed the limitations of counterfactual explanations to recommend actions for algorithmic recourse, and argued for the need of taking causal relationships between features into consideration. Unfortunately, in practice, the true underlying structural causal model is generally unknown. In this work, we first show that it is impossible to guarantee recourse without access to the true structural equations. To address this limitation, we propose two probabilistic approaches to select optimal actions that achieve recourse with high probability given limited causal knowledge (e.g., only the causal graph). The first captures uncertainty over structural equations under additive Gaussian noise, and uses Bayesian model averaging to estimate the counterfactual distribution. The second removes any assumptions on the structural equations by instead computing the average effect of recourse actions on individuals similar to the person who seeks recourse, leading to a novel subpopulation-based interventional notion of recourse. We then derive a gradient-based procedure for selecting optimal recourse actions, and empirically show that the proposed approaches lead to more reliable recommendations under imperfect causal knowledge than non-probabilistic baselines.
Quantitative Propagation of Chaos for SGD in Wide Neural Networks
Authors: Valentin De Bortoli, Alain Durmus, Xavier Fontaine, Umut Simsekli

Abstract:   In this paper, we investigate the limiting behavior of a
  continuous-time counterpart of the Stochastic Gradient Descent (SGD)
  algorithm applied to two-layer overparameterized neural networks, as
  the number or neurons (i.e., the size of the hidden layer)
  $N \to \plusinfty$.  Following a probabilistic approach, we show
  `propagation of chaos' for the particle system defined by this
  continuous-time dynamics under different scenarios, indicating that
  the statistical interaction between the particles asymptotically
  vanishes. In particular, we establish quantitative convergence with
  respect to $N$ of any particle to a solution of a mean-field
  McKean-Vlasov equation in the metric space endowed with the
  Wasserstein distance. In comparison to previous works on the
  subject, we consider settings in which the sequence of stepsizes in
  SGD can potentially depend on the number of neurons and the
  iterations. We then identify two regimes under which different
  mean-field limits are obtained, one of them corresponding to an
  implicitly regularized version of the minimization problem at
  hand. We perform various experiments on real datasets to validate
  our theoretical results, assessing the existence of these two
  regimes on classification problems and illustrating our convergence
  results.
A Causal View on Robustness  of Neural Networks
Authors: Cheng Zhang, Kun Zhang, Yingzhen Li

Abstract: We present a causal view on the robustness of neural networks against input manipulations, which applies not only to traditional classification tasks but also to general measurement data. Based on this view, we design a deep causal manipulation augmented model (deep CAMA) which explicitly models possible manipulations on certain causes leading to changes in the observed effect.  We further develop data augmentation and test-time fine-tuning methods to improve deep CAMA's robustness. When compared with discriminative deep neural networks, our proposed model shows superior robustness against unseen manipulations. As a by-product, our model achieves disentangled representation which separates the representation of manipulations from those of other latent causes.
Minimax Classification with 0-1 Loss and Performance Guarantees
Authors: Santiago Mazuelas, Andrea Zanoni, Aritz Pérez

Abstract: Supervised classification techniques use training samples to find classification rules with small expected 0-1 loss. Conventional methods achieve efficient learning and out-of-sample generalization by minimizing surrogate losses over specific families of rules. This paper presents minimax risk classifiers (MRCs) that do not rely on a choice of surrogate loss and family of rules. MRCs achieve efficient learning and out-of-sample generalization by minimizing worst-case expected 0-1 loss w.r.t. uncertainty sets that are defined by linear constraints and include the true underlying distribution. In addition, MRCs' learning stage provides performance guarantees as lower and upper tight bounds for expected 0-1 loss. We also present MRCs' finite-sample generalization bounds in terms of training size and smallest minimax risk, and show their competitive classification performance w.r.t. state-of-the-art techniques using benchmark datasets.
How to Learn a Useful Critic? Model-based Action-Gradient-Estimator Policy Optimization
Authors: Pierluca D'Oro, Wojciech  Jaśkowski

Abstract: Deterministic-policy actor-critic algorithms for continuous control improve the actor by plugging its actions into the critic and ascending the action-value gradient, which is obtained by chaining the actor's Jacobian matrix with the gradient of the critic with respect to input actions. However, instead of gradients, the critic is, typically, only trained to accurately predict expected returns, which, on their own, are useless for policy optimization. In this paper, we propose MAGE, a model-based actor-critic algorithm, grounded in the theory of policy gradients, which explicitly learns the action-value gradient. MAGE backpropagates through the learned dynamics to compute gradient targets in temporal difference learning, leading to a critic tailored for policy improvement. On a set of MuJoCo continuous-control tasks, we demonstrate the efficiency of the algorithm in comparison to model-free and model-based state-of-the-art baselines.
Coresets for Regressions with Panel Data
Authors: Lingxiao Huang, K Sudhir, Nisheeth Vishnoi

Abstract: A panel dataset contains features or observations for multiple individuals over multiple time periods and regression problems with panel data are common in statistics and applied ML. When dealing with massive datasets, coresets have emerged as a valuable tool from a computational, storage and privacy perspective, as one needs to work with and share much smaller datasets. However, results on coresets for regression problems thus far have only been available for cross-sectional data ($N$ individuals each observed for a single time unit) or longitudinal data (a single individual observed for $T>1$ time units), but there are no results for panel data ($N>1$, $T>1$). This paper introduces the problem of coresets to panel data settings; we first define coresets for several variants of regression problems with panel data and then present efficient algorithms to construct coresets of size that are independent of $N$ and $T$, and only polynomially depend on $1/\varepsilon$ (where $\varepsilon$ is the error parameter) and the number of regression parameters. Our approach is based on the Feldman-Langberg framework in which a key step is to upper bound the “total sensitivity” that is roughly the sum of maximum influences of all individual-time pairs taken over all possible choices of regression parameters. Empirically, we assess our approach with a synthetic and a real-world datasets; the coreset sizes constructed using our approach are much smaller than the full dataset and coresets indeed accelerate the running time of computing the regression objective.
Learning Composable Energy Surrogates for PDE Order Reduction
Authors: Alex Beatson, Jordan Ash, Geoffrey Roeder, Tianju Xue, Ryan P. Adams

Abstract: Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure.
Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs.
To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation.
We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system's total potential energy, which can be approximated by composing these surrogate models. Composable energy surrogates thus permit simulation in the reduced basis of component boundaries. Costly ground-truth simulation of the full structure is avoided, as
training data are generated by performing finite element analysis of individual components. Using dataset aggregation to choose training data allows us to learn energy surrogates which produce accurate macroscopic behavior when composed, accelerating simulation of parametric meta-materials.
Efficient Contextual Bandits with Continuous Actions
Authors: Maryam Majzoubi, Chicheng Zhang, Rajan Chari, Akshay Krishnamurthy, John Langford, Aleksandrs Slivkins

Abstract: We create a computationally tractable learning algorithm for contextual bandits with continuous actions having unknown structure.  The new reduction-style algorithm composes with most supervised learning representations.  We prove that this algorithm works in a general sense and verify the new functionality with large-scale experiments.
Achieving Equalized Odds by Resampling Sensitive Attributes
Authors: Yaniv Romano, Stephen Bates, Emmanuel Candes

Abstract: We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this criterion. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. To rigorously evaluate fitted models, we develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature. Both the model fitting and hypothesis testing leverage a resampled version of the sensitive attribute obeying equalized odds, by construction. We demonstrate the applicability and validity of the proposed framework both in regression and multi-class classification problems, reporting improved performance over state-of-the-art methods. Lastly, we show how to incorporate techniques for equitable uncertainty quantification---unbiased for each group under study---to communicate the results of the data analysis in exact terms.
Multi-Robot Collision Avoidance under Uncertainty with Probabilistic Safety Barrier Certificates
Authors: Wenhao Luo, Wen Sun, Ashish Kapoor

Abstract: Safety in terms of collision avoidance for multi-robot systems is a difficult challenge under uncertainty, non-determinism, and lack of complete information. This paper aims to propose a collision avoidance method that accounts for both measurement uncertainty and motion uncertainty. In particular, we propose Probabilistic Safety Barrier Certificates (PrSBC) using Control Barrier Functions to define the space of admissible control actions that are probabilistically safe with formally provable theoretical guarantee. By formulating the chance constrained safety set into deterministic control constraints with PrSBC, the method entails minimally modifying an existing controller to determine an alternative safe controller via quadratic programming constrained to PrSBC constraints. The key advantage of the approach is that no assumptions about the form of uncertainty are required other than finite support, also enabling worst-case guarantees. We demonstrate effectiveness of the approach through experiments on realistic simulation environments.
Hard Shape-Constrained Kernel Machines
Authors: Pierre-Cyril Aubin-Frankowski, Zoltan Szabo

Abstract: Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape requirements in a hard fashion is an extremely challenging problem. Classically, this task is tackled (i) in a soft way (without out-of-sample guarantees), (ii) by specialized transformation of the variables on a case-by-case basis, or (iii) by using highly restricted function classes, such as polynomials or polynomial splines. In this paper, we prove that hard affine shape constraints on function derivatives can be encoded in kernel machines which represent one of the most flexible and powerful tools in machine learning and statistics. Particularly, we present a tightened second-order cone constrained reformulation, that can be readily implemented in convex solvers. We prove performance guarantees on the solution, and demonstrate the efficiency of the approach in joint quantile regression with applications to economics and to the analysis of aircraft trajectories, among others.
A Closer Look at the Training Strategy for Modern Meta-Learning
Authors: JIAXIN CHEN, Xiao-Ming Wu, Yanke Li, Qimai LI, Li-Ming Zhan, Fu-lai Chung

Abstract: The support/query (S/Q) episodic training strategy has been widely used in modern meta-learning algorithms and is believed to improve their generalization ability to test environments. This paper conducts a theoretical investigation of this training strategy on generalization. From a stability perspective, we analyze the generalization error bound of generic meta-learning algorithms trained with such strategy. We show that the S/Q episodic training strategy naturally leads to a counterintuitive generalization bound of $O(1/\sqrt{n})$, which only depends on the task number $n$ but independent of the inner-task sample size $m$. Under the common assumption $m<
On the Value of Out-of-Distribution Testing: An Example of Goodhart's Law
Authors: Damien Teney, Ehsan Abbasnejad, Kushal Kafle, Robik Shrestha, Christopher Kanan, Anton van den Hengel

Abstract: Out-of-distribution (OOD) testing is increasingly popular for evaluating a machine learning system's ability to generalize beyond the biases of a training set. OOD benchmarks are designed to present a different joint distribution of data and labels between training and test time. VQA-CP has become the standard OOD benchmark for visual question answering, but we discovered three troubling practices in its current use. First, most published methods rely on explicit knowledge of the construction of the OOD splits. They often rely on inverting'' the distribution of labels, e.g. answering mostlyyes'' when the common training answer was ``no''. Second, the OOD test set is used for model selection. Third, a model's in-domain performance is assessed after retraining it on in-domain splits (VQA v2) that exhibit a more balanced distribution of labels. These three practices defeat the objective of evaluating generalization, and put into question the value of methods specifically designed for this dataset. We show that embarrassingly-simple methods, including one that generates answers at random, surpass the state of the art on some question types. We provide short- and long-term solutions to avoid these pitfalls and realize the benefits of OOD evaluation.
Generalised Bayesian Filtering via Sequential Monte Carlo
Authors: Ayman Boustati, Omer Deniz Akyildiz, Theodoros Damoulas, Adam Johansen

Abstract: We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspective of Generalized Bayesian Inference (GBI) to define generalised filtering recursions in HMMs, that can tackle the problem of inference under model misspecification. In doing so, we arrive at principled procedures for robust inference against observation contamination by utilising the $\beta$-divergence. Operationalising the proposed framework is made possible via sequential Monte Carlo methods (SMC), where the standard particle methods, and their associated convergence results, are readily adapted to the new setting. We demonstrate our approach to object tracking and Gaussian process regression problems, and observe improved performance over standard filtering algorithms.
Deterministic Approximation for Submodular Maximization over a Matroid in Nearly Linear Time
Authors: Kai Han, zongmai Cao, Shuang Cui, Benwei Wu

Abstract: We study the problem of maximizing a non-monotone, non-negative submodular function subject to a matroid constraint. The prior best-known deterministic approximation ratio for this problem is $\frac{1}{4}-\epsilon$ under $\mathcal{O}(({n^4}/{\epsilon})\log n)$ time complexity. We show that this deterministic ratio can be improved to $\frac{1}{4}$ under $\mathcal{O}(nr)$ time complexity, and then present a more practical algorithm dubbed TwinGreedyFast which achieves $\frac{1}{4}-\epsilon$ deterministic ratio in nearly-linear running time of $\mathcal{O}(\frac{n}{\epsilon}\log\frac{r}{\epsilon})$. Our approach is based on a novel algorithmic framework of simultaneously constructing two candidate solution sets through greedy search, which enables us to get improved performance bounds by fully exploiting the properties of independence systems. As a byproduct of this framework, we also show that TwinGreedyFast achieves $\frac{1}{2p+2}-\epsilon$ deterministic ratio under a $p$-set system constraint with the same time complexity. To showcase the practicality of our approach, we empirically evaluated the performance of TwinGreedyFast on two network applications, and observed that it outperforms the state-of-the-art deterministic and randomized algorithms with efficient implementations for our problem.
Flows for simultaneous manifold learning and density estimation
Authors: Johann Brehmer, Kyle Cranmer

Abstract: We introduce manifold-learning flows (ℳ-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent data sets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. In a range of experiments we demonstrate how ℳ-flows learn the data manifold and allow for better inference than standard flows in the ambient data space.
Simultaneous Preference and Metric Learning from Paired Comparisons
Authors: Austin Xu, Mark Davenport

Abstract: A popular model of preference in the context of recommendation systems is the so-called ideal point model. In this model, a user is represented as a vector u together with a collection of items x1 ... xN in a common low-dimensional space. The vector u represents the user's "ideal point," or the ideal combination of features that represents a hypothesized most preferred item. The underlying assumption in this model is that a smaller distance between u and an item xj  indicates a stronger preference for xj. In the vast majority of the existing work on learning ideal point models, the underlying distance has been assumed to be Euclidean. However, this eliminates any possibility of interactions between features and a user's underlying preferences. In this paper, we consider the problem of learning an ideal point representation of a user's preferences when the distance metric is an unknown Mahalanobis metric. Specifically, we present a novel approach to estimate the user's ideal point u and the Mahalanobis metric from paired comparisons of the form "item xi is preferred to item xj.'' This can be viewed as a special case of a more general metric learning problem where the location of some points are unknown a priori. We conduct extensive experiments on synthetic and real-world datasets to exhibit the effectiveness of our algorithm.