mtybilly/Instruct2DS huggingface dataset:
Sliced Iterative Normalizing Flows
Authors: Dai, Biwei and Seljak, Uros
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We develop an iterative (greedy) deep learning (DL) algorithm which is able to transform an arbitrary probability distribution function (PDF) into the target PDF. The model is based on iterative Optimal Transport of a series of 1D slices, matching on each slice the marginal PDF to the target. The axes of the orthogonal slices are chosen to maximize the PDF difference using Wasserstein distance at each iteration, which enables the algorithm to scale well to high dimensions. As special cases of this algorithm, we introduce two sliced iterative Normalizing Flow (SINF) models, which map from the data to the latent space (GIS) and vice versa (SIG). We show that SIG is able to generate high quality samples of image datasets, which match the GAN benchmarks, while GIS obtains competitive results on density estimation tasks compared to the density trained NFs, and is more stable, faster, and achieves higher p(x) when trained on small training sets. SINF approach deviates significantly from the current DL paradigm, as it is greedy and does not use concepts such as mini-batching, stochastic gradient descent and gradient back-propagation through deep layers.
Convex Regularization in Monte-Carlo Tree Search
Authors: Dam, Tuan Q and D'Eramo, Carlo and Peters, Jan and Pajarinen, Joni
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Monte-Carlo planning and Reinforcement Learning (RL) are essential to sequential decision making. The recent AlphaGo and AlphaZero algorithms have shown how to successfully combine these two paradigms to solve large-scale sequential decision problems. These methodologies exploit a variant of the well-known UCT algorithm to trade off the exploitation of good actions and the exploration of unvisited states, but their empirical success comes at the cost of poor sample-efficiency and high computation time. In this paper, we overcome these limitations by introducing the use of convex regularization in Monte-Carlo Tree Search (MCTS) to drive exploration efficiently and to improve policy updates. First, we introduce a unifying theory on the use of generic convex regularizers in MCTS, deriving the first regret analysis of regularized MCTS and showing that it guarantees an exponential convergence rate. Second, we exploit our theoretical framework to introduce novel regularized backup operators for MCTS, based on the relative entropy of the policy update and, more importantly, on the Tsallis entropy of the policy, for which we prove superior theoretical guarantees. We empirically verify the consequence of our theoretical results on a toy problem. Finally, we show how our framework can easily be incorporated in AlphaGo and we empirically show the superiority of convex regularization, w.r.t. representative baselines, on well-known RL problems across several Atari games.
Demonstration-Conditioned Reinforcement Learning for Few-Shot Imitation
Authors: Dance, Christopher R. and Perez, Julien and Cachet, Théo
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: In few-shot imitation, an agent is given a few demonstrations of a previously unseen task, and must then successfully perform that task. We propose a novel approach to learning few-shot-imitation agents that we call demonstration-conditioned reinforcement learning (DCRL). Given a training set consisting of demonstrations, reward functions and transition distributions for multiple tasks, the idea is to work with a policy that takes demonstrations as input, and to train this policy to maximize the average of the cumulative reward over the set of training tasks. Relative to previously proposed few-shot imitation methods that use behaviour cloning or infer reward functions from demonstrations, our method has the disadvantage that it requires reward functions at training time. However, DCRL also has several advantages, such as the ability to improve upon suboptimal demonstrations, to operate given state-only demonstrations, and to cope with a domain shift between the demonstrator and the agent. Moreover, we show that DCRL outperforms methods based on behaviour cloning by a large margin, on navigation tasks and on robotic manipulation tasks from the Meta-World benchmark.
Re-understanding Finite-State Representations of Recurrent Policy Networks
Authors: Danesh, Mohamad H and Koul, Anurag and Fern, Alan and Khorram, Saeed
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We introduce an approach for understanding control policies represented as recurrent neural networks. Recent work has approached this problem by transforming such recurrent policy networks into finite-state machines (FSM) and then analyzing the equivalent minimized FSM. While this led to interesting insights, the minimization process can obscure a deeper understanding of a machine’s operation by merging states that are semantically distinct. To address this issue, we introduce an analysis approach that starts with an unminimized FSM and applies more-interpretable reductions that preserve the key decision points of the policy. We also contribute an attention tool to attain a deeper understanding of the role of observations in the decisions. Our case studies on 7 Atari games and 3 control benchmarks demonstrate that the approach can reveal insights that have not been previously noticed.
Newton Method over Networks is Fast up to the Statistical Precision
Authors: Daneshmand, Amir and Scutari, Gesualdo and Dvurechensky, Pavel and Gasnikov, Alexander
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We propose a distributed cubic regularization of the Newton method for solving (constrained) empirical risk minimization problems over a network of agents, modeled as undirected graph. The algorithm employs an inexact, preconditioned Newton step at each agent’s side: the gradient of the centralized loss is iteratively estimated via a gradient-tracking consensus mechanism and the Hessian is subsampled over the local data sets. No Hessian matrices are exchanged over the network. We derive global complexity bounds for convex and strongly convex losses. Our analysis reveals an interesting interplay between sample and iteration/communication complexity: statistically accurate solutions are achievable in roughly the same number of iterations of the centralized cubic Newton, with a communication cost per iteration of the order of $\widetilde\mathcalO\big(1/\sqrt1-h̊o\big)$, where $\o̊$ characterizes the connectivity of the network. This represents a significant improvement with respect to existing, statistically oblivious, distributed Newton-based methods over networks.
BasisDeVAE: Interpretable Simultaneous Dimensionality Reduction and Feature-Level Clustering with Derivative-Based Variational Autoencoders
Authors: Danks, Dominic and Yau, Christopher
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: The Variational Autoencoder (VAE) performs effective nonlinear dimensionality reduction in a variety of problem settings. However, the black-box neural network decoder function typically employed limits the ability of the decoder function to be constrained and interpreted, making the use of VAEs problematic in settings where prior knowledge should be embedded within the decoder. We present DeVAE, a novel VAE-based model with a derivative-based forward mapping, allowing for greater control over decoder behaviour via specification of the decoder function in derivative space. Additionally, we show how DeVAE can be paired with a sparse clustering prior to create BasisDeVAE and perform interpretable simultaneous dimensionality reduction and feature-level clustering. We demonstrate the performance and scalability of the DeVAE and BasisDeVAE models on synthetic and real-world data and present how the derivative-based approach allows for expressive yet interpretable forward models which respect prior knowledge.
Intermediate Layer Optimization for Inverse Problems using Deep Generative Models
Authors: Daras, Giannis and Dean, Joseph and Jalal, Ajil and Dimakis, Alex
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We propose Intermediate Layer Optimization (ILO), a novel optimization algorithm for solving inverse problems with deep generative models. Instead of optimizing only over the initial latent code, we progressively change the input layer obtaining successively more expressive generators. To explore the higher dimensional spaces, our method searches for latent codes that lie within a small l1 ball around the manifold induced by the previous layer. Our theoretical analysis shows that by keeping the radius of the ball relatively small, we can improve the established error bound for compressed sensing with deep generative models. We empirically show that our approach outperforms state-of-the-art methods introduced in StyleGAN2 and PULSE for a wide range of inverse problems including inpainting, denoising, super-resolution and compressed sensing.
Measuring Robustness in Deep Learning Based Compressive Sensing
Authors: Darestani, Mohammad Zalbagi and Chaudhari, Akshay S and Heckel, Reinhard
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that deep-learning-based image reconstruction methods are sensitive to perturbations and are less robust than traditional methods: Neural networks (i) may be sensitive to small, yet adversarially-selected perturbations, (ii) may perform poorly under distribution shifts, and (iii) may fail to recover small but important features in an image. In order to understand the sensitivity to such perturbations, in this work, we measure the robustness of different approaches for image reconstruction including trained and un-trained neural networks as well as traditional sparsity-based methods. We find, contrary to prior works, that both trained and un-trained methods are vulnerable to adversarial perturbations. Moreover, both trained and un-trained methods tuned for a particular dataset suffer very similarly from distribution shifts. Finally, we demonstrate that an image reconstruction method that achieves higher reconstruction quality, also performs better in terms of accurately recovering fine details. Our results indicate that the state-of-the-art deep-learning-based image reconstruction methods provide improved performance than traditional methods without compromising robustness.
SAINT-ACC: Safety-Aware Intelligent Adaptive Cruise Control for Autonomous Vehicles Using Deep Reinforcement Learning
Authors: Das, Lokesh Chandra and Won, Myounggyu
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We present a novel adaptive cruise control (ACC) system namely SAINT-ACC: Safety-Aware Intelligent ACC system (SAINT-ACC) that is designed to achieve simultaneous optimization of traffic efficiency, driving safety, and driving comfort through dynamic adaptation of the inter-vehicle gap based on deep reinforcement learning (RL). A novel dual RL agent-based approach is developed to seek and adapt the optimal balance between traffic efficiency and driving safety/comfort by effectively controlling the driving safety model parameters and inter-vehicle gap based on macroscopic and microscopic traffic information collected from dynamically changing and complex traffic environments. Results obtained through over 12,000 simulation runs with varying traffic scenarios and penetration rates demonstrate that SAINT-ACC significantly enhances traffic flow, driving safety and comfort compared with a state-of-the-art approach.
Lipschitz normalization for self-attention layers with application to graph neural networks
Authors: Dasoulas, George and Scaman, Kevin and Virmaux, Aladin
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Attention based neural networks are state of the art in a large range of applications. However, their performance tends to degrade when the number of layers increases. In this work, we show that enforcing Lipschitz continuity by normalizing the attention scores can significantly improve the performance of deep attention models. First, we show that, for deep graph attention networks (GAT), gradient explosion appears during training, leading to poor performance of gradient-based training algorithms. To address this issue, we derive a theoretical analysis of the Lipschitz continuity of attention modules and introduce LipschitzNorm, a simple and parameter-free normalization for self-attention mechanisms that enforces the model to be Lipschitz continuous. We then apply LipschitzNorm to GAT and Graph Transformers and show that their performance is substantially improved in the deep setting (10 to 30 layers). More specifically, we show that a deep GAT model with LipschitzNorm achieves state of the art results for node label prediction tasks that exhibit long-range dependencies, while showing consistent improvements over their unnormalized counterparts in benchmark node classification tasks.
Householder Sketch for Accurate and Accelerated Least-Mean-Squares Solvers
Authors: Dass, Jyotikrishna and Mahapatra, Rabi
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Least-Mean-Squares (\textscLMS) solvers comprise a class of fundamental optimization problems such as linear regression, and regularized regressions such as Ridge, LASSO, and Elastic-Net. Data summarization techniques for big data generate summaries called coresets and sketches to speed up model learning under streaming and distributed settings. For example, i̧tepnips2019 design a fast and accurate Caratheodory set on input data to boost the performance of existing \textscLMS solvers. In retrospect, we explore classical Householder transformation as a candidate for sketching and accurately solving LMS problems. We find it to be a simpler, memory-efficient, and faster alternative that always existed to the above strong baseline. We also present a scalable algorithm based on the construction of distributed Householder sketches to solve \textscLMS problem across multiple worker nodes. We perform thorough empirical analysis with large synthetic and real datasets to evaluate the performance of Householder sketch and compare with \ţepnips2019. Our results show Householder sketch speeds up existing \textscLMS solvers in the scikit-learn library up to $100$x-$400$x. Also, it is $10$x-$100$x faster than the above baseline with similar numerical stability. The distributed algorithm demonstrates linear scalability with a near-negligible communication overhead.
Byzantine-Resilient High-Dimensional SGD with Local Iterations on Heterogeneous Data
Authors: Data, Deepesh and Diggavi, Suhas
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We study stochastic gradient descent (SGD) with local iterations in the presence of Byzantine clients, motivated by the federated learning. The clients, instead of communicating with the server in every iteration, maintain their local models, which they update by taking several SGD iterations based on their own datasets and then communicate the net update with the server, thereby achieving communication-efficiency. Furthermore, only a subset of clients communicates with the server at synchronization times. The Byzantine clients may collude and send arbitrary vectors to the server to disrupt the learning process. To combat the adversary, we employ an efficient high-dimensional robust mean estimation algorithm at the server to filter-out corrupt vectors; and to analyze the outlier-filtering procedure, we develop a novel matrix concentration result that may be of independent interest. We provide convergence analyses for both strongly-convex and non-convex smooth objectives in the heterogeneous data setting. We believe that ours is the first Byzantine-resilient local SGD algorithm and analysis with non-trivial guarantees. We corroborate our theoretical results with preliminary experiments for neural network training.
Catformer: Designing Stable Transformers via Sensitivity Analysis
Authors: Davis, Jared Q and Gu, Albert and Choromanski, Krzysztof and Dao, Tri and Re, Christopher and Finn, Chelsea and Liang, Percy
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Transformer architectures are widely used, but training them is non-trivial, requiring custom learning rate schedules, scaling terms, residual connections, careful placement of submodules such as normalization, and so on. In this paper, we improve upon recent analysis of Transformers and formalize a notion of sensitivity to capture the difficulty of training. Sensitivity characterizes how the variance of activation and gradient norms change in expectation when parameters are randomly perturbed. We analyze the sensitivity of previous Transformer architectures and design a new architecture, the Catformer, which replaces residual connections or RNN-based gating mechanisms with concatenation. We prove that Catformers are less sensitive than other Transformer variants and demonstrate that this leads to more stable training. On DMLab30, a suite of high-dimension reinforcement tasks, Catformer outperforms other transformers, including Gated Transformer-XL—the state-of-the-art architecture designed to address stability—by 13%.
Diffusion Source Identification on Networks with Statistical Confidence
Authors: Dawkins, Quinlan E and Li, Tianxi and Xu, Haifeng
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Diffusion source identification on networks is a problem of fundamental importance in a broad class of applications, including controlling the spreading of rumors on social media, identifying a computer virus over cyber networks, or identifying the disease center during epidemiology. Though this problem has received significant recent attention, most known approaches are well-studied in only very restrictive settings and lack theoretical guarantees for more realistic networks. We introduce a statistical framework for the study of this problem and develop a confidence set inference approach inspired by hypothesis testing. Our method efficiently produces a small subset of nodes, which provably covers the source node with any pre-specified confidence level without restrictive assumptions on network structures. To our knowledge, this is the first diffusion source identification method with a practically useful theoretical guarantee on general networks. We demonstrate our approach via extensive synthetic experiments on well-known random network models, a large data set of real-world networks as well as a mobility network between cities concerning the COVID-19 spreading in January 2020.
Bayesian Deep Learning via Subnetwork Inference
Authors: Daxberger, Erik and Nalisnick, Eric and Allingham, James U and Antoran, Javier and Hernandez-Lobato, Jose Miguel
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace as a simple, scalable Bayesian deep learning method: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork using the linearized Laplace approximation. We propose a subnetwork selection strategy that aims to maximally preserve the model’s predictive uncertainty. Empirically, our approach compares favorably to ensembles and less expressive posterior approximations over full networks.
Adversarial Robustness Guarantees for Random Deep Neural Networks
Authors: De Palma, Giacomo and Kiani, Bobak and Lloyd, Seth
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of adversarial examples for deep neural networks with random weights and biases, and prove that for any p$≥$1, the \ell^p distance of any given input from the classification boundary scales as one over the square root of the dimension of the input times the \ell^p norm of the input. The results are based on the recently proved equivalence between Gaussian processes and deep neural networks in the limit of infinite width of the hidden layers, and are validated with experiments on both random deep neural networks and deep neural networks trained on the MNIST and CIFAR10 datasets. The results constitute a fundamental advance in the theoretical understanding of adversarial examples, and open the way to a thorough theoretical characterization of the relation between network architecture and robustness to adversarial perturbations.
High-Dimensional Gaussian Process Inference with Derivatives
Authors: de Roos, Filip and Gessner, Alexandra and Hennig, Philipp
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Although it is widely known that Gaussian processes can be conditioned on observations of the gradient, this functionality is of limited use due to the prohibitive computational cost of $\mathcalO(N^3 D^3)$ in data points $N$ and dimension $D$. The dilemma of gradient observations is that a single one of them comes at the same cost as $D$ independent function evaluations, so the latter are often preferred. Careful scrutiny reveals, however, that derivative observations give rise to highly structured kernel Gram matrices for very general classes of kernels (inter alia, stationary kernels). We show that in the \emphlow-data regime $N < D$, the Gram matrix can be decomposed in a manner that reduces the cost of inference to $\mathcalO(N^2D + (N^2)^3)$ (i.e., linear in the number of dimensions) and, in special cases, to $\mathcalO(N^2D + N^3)$. This reduction in complexity opens up new use-cases for inference with gradients especially in the high-dimensional regime, where the information-to-cost ratio of gradient observations significantly increases. We demonstrate this potential in a variety of tasks relevant for machine learning, such as optimization and Hamiltonian Monte Carlo with predictive gradients.
Transfer-Based Semantic Anomaly Detection
Authors: Deecke, Lucas and Ruff, Lukas and Vandermeulen, Robert A. and Bilen, Hakan
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Detecting semantic anomalies is challenging due to the countless ways in which they may appear in real-world data. While enhancing the robustness of networks may be sufficient for modeling simplistic anomalies, there is no good known way of preparing models for all potential and unseen anomalies that can potentially occur, such as the appearance of new object classes. In this paper, we show that a previously overlooked strategy for anomaly detection (AD) is to introduce an explicit inductive bias toward representations transferred over from some large and varied semantic task. We rigorously verify our hypothesis in controlled trials that utilize intervention, and show that it gives rise to surprisingly effective auxiliary objectives that outperform previous AD paradigms.
Grid-Functioned Neural Networks
Authors: Dehesa, Javier and Vidler, Andrew and Padget, Julian and Lutteroth, Christof
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We introduce a new neural network architecture that we call "grid-functioned" neural networks. It utilises a grid structure of network parameterisations that can be specialised for different subdomains of the problem, while maintaining smooth, continuous behaviour. The grid gives the user flexibility to prevent gross features from overshadowing important minor ones. We present a full characterisation of its computational and spatial complexity, and demonstrate its potential, compared to a traditional architecture, over a set of synthetic regression problems. We further illustrate the benefits through a real-world 3D skeletal animation case study, where it offers the same visual quality as a state-of-the-art model, but with lower computational complexity and better control accuracy.
Multidimensional Scaling: Approximation and Complexity
Authors: Demaine, Erik and Hesterberg, Adam and Koehler, Frederic and Lynch, Jayson and Urschel, John
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Metric Multidimensional scaling (MDS) is a classical method for generating meaningful (non-linear) low-dimensional embeddings of high-dimensional data. MDS has a long history in the statistics, machine learning, and graph drawing communities. In particular, the Kamada-Kawai force-directed graph drawing method is equivalent to MDS and is one of the most popular ways in practice to embed graphs into low dimensions. Despite its ubiquity, our theoretical understanding of MDS remains limited as its objective function is highly non-convex. In this paper, we prove that minimizing the Kamada-Kawai objective is NP-hard and give a provable approximation algorithm for optimizing it, which in particular is a PTAS on low-diameter graphs. We supplement this result with experiments suggesting possible connections between our greedy approximation algorithm and gradient-based methods.
What Does Rotation Prediction Tell Us about Classifier Accuracy under Varying Testing Environments?
Authors: Deng, Weijian and Gould, Stephen and Zheng, Liang
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Understanding classifier decision under novel environments is central to the community, and a common practice is evaluating it on labeled test sets. However, in real-world testing, image annotations are difficult and expensive to obtain, especially when the test environment is changing. A natural question then arises: given a trained classifier, can we evaluate its accuracy on varying unlabeled test sets? In this work, we train semantic classification and rotation prediction in a multi-task way. On a series of datasets, we report an interesting finding, i.e., the semantic classification accuracy exhibits a strong linear relationship with the accuracy of the rotation prediction task (Pearson’s Correlation r > 0.88). This finding allows us to utilize linear regression to estimate classifier performance from the accuracy of rotation prediction which can be obtained on the test set through the freely generated rotation labels.
Toward Better Generalization Bounds with Locally Elastic Stability
Authors: Deng, Zhun and He, Hangfeng and Su, Weijie
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emphuniform stability is arguably the most popular one, which yields exponential generalization bounds. However, uniform stability only considers the worst-case loss change (or so-called sensitivity) by removing a single data point, which is distribution-independent and therefore undesirable. There are many cases that the worst-case sensitivity of the loss is much larger than the average sensitivity taken over the single data point that is removed, especially in some advanced models such as random feature models or neural networks. Many previous works try to mitigate the distribution independent issue by proposing weaker notions of stability, however, they either only yield polynomial bounds or the bounds derived do not vanish as sample size goes to infinity. Given that, we propose \emphlocally elastic stability as a weaker and distribution-dependent stability notion, which still yields exponential generalization bounds. We further demonstrate that locally elastic stability implies tighter generalization bounds than those derived based on uniform stability in many situations by revisiting the examples of bounded support vector machines, regularized least square regressions, and stochastic gradient descent.
Revenue-Incentive Tradeoffs in Dynamic Reserve Pricing
Authors: Deng, Yuan and Lahaie, Sebastien and Mirrokni, Vahab and Zuo, Song
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Online advertisements are primarily sold via repeated auctions with reserve prices. In this paper, we study how to set reserves to boost revenue based on the historical bids of strategic buyers, while controlling the impact of such a policy on the incentive compatibility of the repeated auctions. Adopting an incentive compatibility metric which quantifies the incentives to shade bids, we propose a novel class of reserve pricing policies and provide analytical tradeoffs between their revenue performance and bid-shading incentives. The policies are inspired by the exponential mechanism from the literature on differential privacy, but our study uncovers mechanisms with significantly better revenue-incentive tradeoffs than the exponential mechanism in practice. We further empirically evaluate the tradeoffs on synthetic data as well as real ad auction data from a major ad exchange to verify and support our theoretical findings.
Heterogeneity for the Win: One-Shot Federated Clustering
Authors: Dennis, Don Kurian and Li, Tian and Smith, Virginia
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: In this work, we explore the unique challenges—and opportunities—of unsupervised federated learning (FL). We develop and analyze a one-shot federated clustering scheme, kfed, based on the widely-used Lloyd’s method for $k$-means clustering. In contrast to many supervised problems, we show that the issue of statistical heterogeneity in federated networks can in fact benefit our analysis. We analyse kfed under a center separation assumption and compare it to the best known requirements of its centralized counterpart. Our analysis shows that in heterogeneous regimes where the number of clusters per device $(k’)$ is smaller than the total number of clusters over the network $k$, $(k’łe \sqrtk)$, we can use heterogeneity to our advantage—significantly weakening the cluster separation requirements for kfed. From a practical viewpoint, kfed also has many desirable properties: it requires only round of communication, can run asynchronously, and can handle partial participation or node/network failures. We motivate our analysis with experiments on common FL benchmarks, and highlight the practical utility of one-shot clustering through use-cases in personalized FL and device sampling.
Kernel Continual Learning
Authors: Derakhshani, Mohammad Mahdi and Zhen, Xiantong and Shao, Ling and Snoek, Cees
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that stores a subset of samples for each task to learn task-specific classifiers based on kernel ridge regression. This does not require memory replay and systematically avoids task interference in the classifiers. We further introduce variational random features to learn a data-driven kernel for each task. To do so, we formulate kernel continual learning as a variational inference problem, where a random Fourier basis is incorporated as the latent variable. The variational posterior distribution over the random Fourier basis is inferred from the coreset of each task. In this way, we are able to generate more informative kernels specific to each task, and, more importantly, the coreset size can be reduced to achieve more compact memory, resulting in more efficient continual learning based on episodic memory. Extensive evaluation on four benchmarks demonstrates the effectiveness and promise of kernels for continual learning.
Bayesian Optimization over Hybrid Spaces
Authors: Deshwal, Aryan and Belakaria, Syrine and Doppa, Janardhan Rao
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design optimization via lab experiments, discrete and continuous variables correspond to the presence/absence of primitive elements and their relative concentrations respectively. The key challenge is to accurately model the complex interactions between discrete and continuous variables. In this paper, we propose a novel approach referred as Hybrid Bayesian Optimization (HyBO) by utilizing diffusion kernels, which are naturally defined over continuous and discrete variables. We develop a principled approach for constructing diffusion kernels over hybrid spaces by utilizing the additive kernel formulation, which allows additive interactions of all orders in a tractable manner. We theoretically analyze the modeling strength of additive hybrid kernels and prove that it has the universal approximation property. Our experiments on synthetic and six diverse real-world benchmarks show that HyBO significantly outperforms the state-of-the-art methods.
Navigation Turing Test (NTT): Learning to Evaluate Human-Like Navigation
Authors: Devlin, Sam and Georgescu, Raluca and Momennejad, Ida and Rzepecki, Jaroslaw and Zuniga, Evelyn and Costello, Gavin and Leroy, Guy and Shaw, Ali and Hofmann, Katja
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: A key challenge on the path to developing agents that learn complex human-like behavior is the need to quickly and accurately quantify human-likeness. While human assessments of such behavior can be highly accurate, speed and scalability are limited. We address these limitations through a novel automated Navigation Turing Test (ANTT) that learns to predict human judgments of human-likeness. We demonstrate the effectiveness of our automated NTT on a navigation task in a complex 3D environment. We investigate six classification models to shed light on the types of architectures best suited to this task, and validate them against data collected through a human NTT. Our best models achieve high accuracy when distinguishing true human and agent behavior. At the same time, we show that predicting finer-grained human assessment of agents’ progress towards human-like behavior remains unsolved. Our work takes an important step towards agents that more effectively learn complex human-like behavior.
Versatile Verification of Tree Ensembles
Authors: Devos, Laurens and Meert, Wannes and Davis, Jesse
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Machine learned models often must abide by certain requirements (e.g., fairness or legal). This has spurred interested in developing approaches that can provably verify whether a model satisfies certain properties. This paper introduces a generic algorithm called Veritas that enables tackling multiple different verification tasks for tree ensemble models like random forests (RFs) and gradient boosted decision trees (GBDTs). This generality contrasts with previous work, which has focused exclusively on either adversarial example generation or robustness checking. Veritas formulates the verification task as a generic optimization problem and introduces a novel search space representation. Veritas offers two key advantages. First, it provides anytime lower and upper bounds when the optimization problem cannot be solved exactly. In contrast, many existing methods have focused on exact solutions and are thus limited by the verification problem being NP-complete. Second, Veritas produces full (bounded suboptimal) solutions that can be used to generate concrete examples. We experimentally show that our method produces state-of-the-art robustness estimates, especially when executed with strict time constraints. This is exceedingly important when checking the robustness of large datasets. Additionally, we show that Veritas enables tackling more real-world verification scenarios.
On the Inherent Regularization Effects of Noise Injection During Training
Authors: Dhifallah, Oussama and Lu, Yue
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Randomly perturbing networks during the training process is a commonly used approach to improving generalization performance. In this paper, we present a theoretical study of one particular way of random perturbation, which corresponds to injecting artificial noise to the training data. We provide a precise asymptotic characterization of the training and generalization errors of such randomly perturbed learning problems on a random feature model. Our analysis shows that Gaussian noise injection in the training process is equivalent to introducing a weighted ridge regularization, when the number of noise injections tends to infinity. The explicit form of the regularization is also given. Numerical results corroborate our asymptotic predictions, showing that they are accurate even in moderate problem dimensions. Our theoretical predictions are based on a new correlated Gaussian equivalence conjecture that generalizes recent results in the study of random feature models.
Hierarchical Agglomerative Graph Clustering in Nearly-Linear Time
Authors: Dhulipala, Laxman and Eisenstat, David and Łącki, Jakub and Mirrokni, Vahab and Shi, Jessica
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We study the widely-used hierarchical agglomerative clustering (HAC) algorithm on edge-weighted graphs. We define an algorithmic framework for hierarchical agglomerative graph clustering that provides the first efficient $\tildeO(m)$ time exact algorithms for classic linkage measures, such as complete- and WPGMA-linkage, as well as other measures. Furthermore, for average-linkage, arguably the most popular variant of HAC, we provide an algorithm that runs in $\tildeO(n\sqrtm)$ time. For this variant, this is the first exact algorithm that runs in subquadratic time, as long as $m=n^2-ε$ for some constant $ε > 0$. We complement this result with a simple $ε$-close approximation algorithm for average-linkage in our framework that runs in $\tildeO(m)$ time. As an application of our algorithms, we consider clustering points in a metric space by first using $k$-NN to generate a graph from the point set, and then running our algorithms on the resulting weighted graph. We validate the performance of our algorithms on publicly available datasets, and show that our approach can speed up clustering of point datasets by a factor of 20.7–76.5x.
Learning Online Algorithms with Distributional Advice
Authors: Diakonikolas, Ilias and Kontonis, Vasilis and Tzamos, Christos and Vakilian, Ali and Zarifis, Nikos
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We study the problem of designing online algorithms given advice about the input. While prior work had focused on deterministic advice, we only assume distributional access to the instances of interest, and the goal is to learn a competitive algorithm given access to i.i.d. samples. We aim to be competitive against an adversary with prior knowledge of the distribution, while also performing well against worst-case inputs. We focus on the classical online problems of ski-rental and prophet-inequalities, and provide sample complexity bounds for the underlying learning tasks. First, we point out that for general distributions it is information-theoretically impossible to beat the worst-case competitive-ratio with any finite sample size. As our main contribution, we establish strong positive results for well-behaved distributions. Specifically, for the broad class of log-concave distributions, we show that $\mathrmpoly(1/ε)$ samples suffice to obtain $(1+ε)$-competitive ratio. Finally, we show that this sample upper bound is close to best possible, even for very simple classes of distributions.
A Wasserstein Minimax Framework for Mixed Linear Regression
Authors: Diamandis, Theo and Eldar, Yonina and Fallah, Alireza and Farnia, Farzan and Ozdaglar, Asuman
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems, Wasserstein Mixed Linear Regression (WMLR), which minimizes the Wasserstein distance between the learned and target mixture regression models. Through a model-based duality analysis, WMLR reduces the underlying MLR task to a nonconvex-concave minimax optimization problem, which can be provably solved to find a minimax stationary point by the Gradient Descent Ascent (GDA) algorithm. In the special case of mixtures of two linear regression models, we show that WMLR enjoys global convergence and generalization guarantees. We prove that WMLR’s sample complexity grows linearly with the dimension of data. Finally, we discuss the application of WMLR to the federated learning task where the training samples are collected by multiple agents in a network. Unlike the Expectation-Maximization algorithm, WMLR directly extends to the distributed, federated learning setting. We support our theoretical results through several numerical experiments, which highlight our framework’s ability to handle the federated learning setting with mixture models.
Context-Aware Online Collective Inference for Templated Graphical Models
Authors: Dickens, Charles and Pryor, Connor and Augustine, Eriq and Miller, Alexander and Getoor, Lise
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: In this work, we examine online collective inference, the problem of maintaining and performing inference over a sequence of evolving graphical models. We utilize templated graphical models (TGM), a general class of graphical models expressed via templates and instantiated with data. A key challenge is minimizing the cost of instantiating the updated model. To address this, we define a class of exact and approximate context-aware methods for updating an existing TGM. These methods avoid a full re-instantiation by using the context of the updates to only add relevant components to the graphical model. Further, we provide stability bounds for the general online inference problem and regret bounds for a proposed approximation. Finally, we implement our approach in probabilistic soft logic, and test it on several online collective inference tasks. Through these experiments we verify the bounds on regret and stability, and show that our approximate online approach consistently runs two to five times faster than the offline alternative while, surprisingly, maintaining the quality of the predictions.
ARMS: Antithetic-REINFORCE-Multi-Sample Gradient for Binary Variables
Authors: Dimitriev, Aleksandar and Zhou, Mingyuan
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Estimating the gradients for binary variables is a task that arises frequently in various domains, such as training discrete latent variable models. What has been commonly used is a REINFORCE based Monte Carlo estimation method that uses either independent samples or pairs of negatively correlated samples. To better utilize more than two samples, we propose ARMS, an Antithetic REINFORCE-based Multi-Sample gradient estimator. ARMS uses a copula to generate any number of mutually antithetic samples. It is unbiased, has low variance, and generalizes both DisARM, which we show to be ARMS with two samples, and the leave-one-out REINFORCE (LOORF) estimator, which is ARMS with uncorrelated samples. We evaluate ARMS on several datasets for training generative models, and our experimental results show that it outperforms competing methods. We also develop a version of ARMS for optimizing the multi-sample variational bound, and show that it outperforms both VIMCO and DisARM. The code is publicly available.
XOR-CD: Linearly Convergent Constrained Structure Generation
Authors: Ding, Fan and Ma, Jianzhu and Xu, Jinbo and Xue, Yexiang
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We propose XOR-Contrastive Divergence learning (XOR-CD), a provable approach for constrained structure generation, which remains difficult for state-of-the-art neural network and constraint reasoning approaches. XOR-CD harnesses XOR-Sampling to generate samples from the model distribution in CD learning and is guaranteed to generate valid structures. In addition, XOR-CD has a linear convergence rate towards the global maximum of the likelihood function within a vanishing constant in learning exponential family models. Constraint satisfaction enabled by XOR-CD also boosts its learning performance. Our real-world experiments on data-driven experimental design, dispatching route generation, and sequence-based protein homology detection demonstrate the superior performance of XOR-CD compared to baseline approaches in generating valid structures as well as capturing the inductive bias in the training set.