Few-Bit Backward: Quantized Gradients of Activation Functions for Memory Footprint Reduction.

Georgii Novikov, Daniel Bershatsky, Julia Gusak, Alex Shonenkov, Denis Dimitrov, Ivan Oseledets

Abstract: Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few pointwise nonlinearities in its architecture, and such operation induces additional memory costs which -- as we show -- can be significantly reduced by quantization of the gradients. We propose a systematic approach to compute optimal quantization of the retained gradients of the pointwise nonlinear functions with only a few bits per each element. We show that such approximation can be achieved by computing optimal piecewise-constant approximation of the derivative of the activation function, which can be done by dynamic programming. The drop-in replacements are implemented for all popular nonlinearities and can be used in any existing pipeline. We confirm the memory reduction and the same convergence on several open benchmarks.


Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra.

Liang Liao, Sen Lin, Lun Li, Xiuwei Zhang, Song Zhao, Yan Wang, Xinqiang Wang, Qi Gao, Jingyu Wang

Abstract: Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order input into a matrix or break it into a series of order-two slices to tackle higher order data such as multispectral images and videos with the SVD. Higher order singular value decomposition (HOSVD) extends the SVD and can approximate higher order data using sums of a few rank-one components. We consider the problem of generalizing HOSVD over a finite dimensional commutative algebra. This algebra, referred to as a t-algebra, generalizes the field of complex numbers. The elements of the algebra, called t-scalars, are fix-sized arrays of complex numbers. One can generalize matrices and tensors over t-scalars and then extend many canonical matrix and tensor algorithms, including HOSVD, to obtain higher-performance versions. The generalization of HOSVD is called THOSVD. Its performance of approximating multi-way data can be further improved by an alternating algorithm. THOSVD also unifies a wide range of principal component analysis algorithms. To exploit the potential of generalized algorithms using t-scalars for approximating images, we use a pixel neighborhood strategy to convert each pixel to "deeper-order" t-scalar. Experiments on publicly available images show that the generalized algorithm over t-scalars, namely THOSVD, compares favorably with its canonical counterparts.


LocUNet: Fast Urban Positioning Using Radio Maps and Deep Learning.

Çağkan Yapar, Ron Levie, Gitta Kutyniok, Giuseppe Caire

Abstract: This paper deals with the problem of localization in a cellular network in a dense urban scenario. Global Navigation Satellite Systems (GNSS) typically perform poorly in urban environments, where the likelihood of line-of-sight conditions is low, and thus alternative localization methods are required for good accuracy. We present LocUNet: A deep learning method for localization, based merely on Received Signal Strength (RSS) from Base Stations (BSs), which does not require any increase in computation complexity at the user devices with respect to the device standard operations, unlike methods that rely on time of arrival or angle of arrival information. In the proposed method, the user to be localized reports the RSS from BSs to a Central Processing Unit (CPU), which may be located in the cloud. Alternatively, the localization can be performed locally at the user. Using estimated pathloss radio maps of the BSs, LocUNet can localize users with state-of-the-art accuracy and enjoys high robustness to inaccuracies in the radio maps. The proposed method does not require pre-sampling of the environment; and is suitable for real-time applications, thanks to the RadioUNet, a neural network-based radio map estimator. We also introduce two datasets that allow numerical comparisons of RSS and Time of Arrival (ToA) methods in realistic urban environments.


KSD Aggregated Goodness-of-fit Test.

Antonin Schrab, Benjamin Guedj, Arthur Gretton

Abstract: We investigate properties of goodness-of-fit tests based on the Kernel Stein Discrepancy (KSD). We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. KSDAgg avoids splitting the data to perform kernel selection (which leads to a loss in test power), and rather maximises the test power over a collection of kernels. We provide theoretical guarantees on the power of KSDAgg: we show it achieves the smallest uniform separation rate of the collection, up to a logarithmic term. KSDAgg can be computed exactly in practice as it relies either on a parametric bootstrap or on a wild bootstrap to estimate the quantiles and the level corrections. In particular, for the crucial choice of bandwidth of a fixed kernel, it avoids resorting to arbitrary heuristics (such as median or standard deviation) or to data splitting. We find on both synthetic and real-world data that KSDAgg outperforms other state-of-the-art adaptive KSD-based goodness-of-fit testing procedures.


Algorithms for Efficiently Learning Low-Rank Neural Networks.

Kiran Vodrahalli, Rakesh Shivanna, Maheswaran Sathiamoorthy, Sagar Jain, Ed H. Chi

Abstract: We study algorithms for learning low-rank neural networks -- networks where the weight parameters are re-parameterized by products of two low-rank matrices. First, we present a provably efficient algorithm which learns an optimal low-rank approximation to a single-hidden-layer ReLU network up to additive error $\epsilon$ with probability $\ge 1 - \delta$, given access to noiseless samples with Gaussian marginals in polynomial time and samples. Thus, we provide the first example of an algorithm which can efficiently learn a neural network up to additive error without assuming the ground truth is realizable. To solve this problem, we introduce an efficient SVD-based $\textit{Nonlinear Kernel Projection}$ algorithm for solving a nonlinear low-rank approximation problem over Gaussian space. Inspired by the efficiency of our algorithm, we propose a novel low-rank initialization framework for training low-rank $\textit{deep}$ networks, and prove that for ReLU networks, the gap between our method and existing schemes widens as the desired rank of the approximating weights decreases, or as the dimension of the inputs increases (the latter point holds when network width is superlinear in dimension). Finally, we validate our theory by training ResNet and EfficientNet models on ImageNet.


Auto-Transfer: Learning to Route Transferrable Representations.

Keerthiram Murugesan, Vijay Sadashivaiah, Ronny Luss, Karthikeyan Shanmugam, Pin-Yu Chen, Amit Dhurandhar

Abstract: Knowledge transfer between heterogeneous source and target networks and tasks has received a lot of attention in recent times as large amounts of quality labelled data can be difficult to obtain in many applications. Existing approaches typically constrain the target deep neural network (DNN) feature representations to be close to the source DNNs feature representations, which can be limiting. We, in this paper, propose a novel adversarial multi-armed bandit approach which automatically learns to route source representations to appropriate target representations following which they are combined in meaningful ways to produce accurate target models. We see upwards of 5% accuracy improvements compared with the state-of-the-art knowledge transfer methods on four benchmark (target) image datasets CUB200, Stanford Dogs, MIT67, and Stanford40 where the source dataset is ImageNet. We qualitatively analyze the goodness of our transfer scheme by showing individual examples of the important features our target network focuses on in different layers compared with the (closest) competitors. We also observe that our improvement over other methods is higher for smaller target datasets making it an effective tool for small data applications that may benefit from transfer learning.


VOS: Learning What You Don't Know by Virtual Outlier Synthesis.

Xuefeng Du, Zhaoning Wang, Mu Cai, Yixuan Li

Abstract: Out-of-distribution (OOD) detection has received much attention lately due to its importance in the safe deployment of neural networks. One of the key challenges is that models lack supervision signals from unknown data, and as a result, can produce overconfident predictions on OOD data. Previous approaches rely on real outlier datasets for model regularization, which can be costly and sometimes infeasible to obtain in practice. In this paper, we present VOS, a novel framework for OOD detection by adaptively synthesizing virtual outliers that can meaningfully regularize the model's decision boundary during training. Specifically, VOS samples virtual outliers from the low-likelihood region of the class-conditional distribution estimated in the feature space. Alongside, we introduce a novel unknown-aware training objective, which contrastively shapes the uncertainty space between the ID data and synthesized outlier data. VOS achieves state-of-the-art performance on both object detection and image classification models, reducing the FPR95 by up to 7.87% compared to the previous best method. Code is available at https://github.com/deeplearning-wisc/vos.


On the Benefits of Selectivity in Pseudo-Labeling for Unsupervised Multi-Source-Free Domain Adaptation.

Abstract: Due to privacy, storage, and other constraints, there is a growing need for unsupervised domain adaptation techniques in machine learning that do not require access to the data used to train a collection of source models. Existing methods for such multi-source-free domain adaptation typically train a target model using supervised techniques in conjunction with pseudo-labels for the target data, which are produced by the available source models. However, we show that assigning pseudo-labels to only a subset of the target data leads to improved performance. In particular, we develop an information-theoretic bound on the generalization error of the resulting target model that demonstrates an inherent bias-variance trade-off controlled by the subset choice. Guided by this analysis, we develop a method that partitions the target data into pseudo-labeled and unlabeled subsets to balance the trade-off. In addition to exploiting the pseudo-labeled subset, our algorithm further leverages the information in the unlabeled subset via a traditional unsupervised domain adaptation feature alignment procedure. Experiments on multiple benchmark datasets demonstrate the superior performance of the proposed method.


Unpaired Image Super-Resolution with Optimal Transport Maps.

Milena Gazdieva, Litu Rout, Alexander Korotin, Alexander Filippov, Evgeny Burnaev

Abstract: Real-world image super-resolution (SR) tasks often do not have paired datasets limiting the application of supervised techniques. As a result, the tasks are usually approached by unpaired techniques based on Generative Adversarial Networks (GANs) which yield complex training losses with several regularization terms such as content and identity losses. We theoretically investigate the optimization problems which arise in such models and find two surprising observations. First, the learned SR map is always an optimal transport (OT) map. Second, we empirically show that the learned map is biased, i.e., it may not actually transform the distribution of low-resolution images to high-resolution images. Inspired by these findings, we propose an algorithm for unpaired SR which learns an unbiased OT map for the perceptual transport cost. Unlike existing GAN-based alternatives, our algorithm has a simple optimization objective reducing the neccesity to perform complex hyperparameter selection and use additional regularizations. At the same time, it provides nearly state-of-the-art performance on the large-scale unpaired AIM-19 dataset.


Deep Layer-wise Networks Have Closed-Form Weights.

Chieh Wu, Aria Masoomi, Arthur Gretton, Jennifer Dy

Abstract: There is currently a debate within the neuroscience community over the likelihood of the brain performing backpropagation (BP). To better mimic the brain, training a network \textit{one layer at a time} with only a "single forward pass" has been proposed as an alternative to bypass BP; we refer to these networks as "layer-wise" networks. We continue the work on layer-wise networks by answering two outstanding questions. First, $\textit{do they have a closed-form solution?}$ Second, $\textit{how do we know when to stop adding more layers?}$ This work proves that the Kernel Mean Embedding is the closed-form weight that achieves the network global optimum while driving these networks to converge towards a highly desirable kernel for classification; we call it the $\textit{Neural Indicator Kernel}$.


Parameters or Privacy: A Provable Tradeoff Between Overparameterization and Membership Inference.

Jasper Tan, Blake Mason, Hamid Javadi, Richard G. Baraniuk

Abstract: A surprising phenomenon in modern machine learning is the ability of a highly overparameterized model to generalize well (small error on the test data) even when it is trained to memorize the training data (zero error on the training data). This has led to an arms race towards increasingly overparameterized models (c.f., deep learning). In this paper, we study an underexplored hidden cost of overparameterization: the fact that overparameterized models are more vulnerable to privacy attacks, in particular the membership inference attack that predicts the (potentially sensitive) examples used to train a model. We significantly extend the relatively few empirical results on this problem by theoretically proving for an overparameterized linear regression model with Gaussian data that the membership inference vulnerability increases with the number of parameters. Moreover, a range of empirical studies indicates that more complex, nonlinear models exhibit the same behavior. Finally, we study different methods for mitigating such attacks in the overparameterized regime, such as noise addition and regularization, and conclude that simply reducing the parameters of an overparameterized model is an effective strategy to protect it from membership inference without greatly decreasing its generalization error.


NoisyMix: Boosting Robustness by Combining Data Augmentations, Stability Training, and Noise Injections.

N. Benjamin Erichson, Soon Hoe Lim, Francisco Utrera, Winnie Xu, Ziang Cao, Michael W. Mahoney

Abstract: For many real-world applications, obtaining stable and robust statistical performance is more important than simply achieving state-of-the-art predictive test accuracy, and thus robustness of neural networks is an increasingly important topic. Relatedly, data augmentation schemes have been shown to improve robustness with respect to input perturbations and domain shifts. Motivated by this, we introduce NoisyMix, a training scheme that combines data augmentations with stability training and noise injections to improve both model robustness and in-domain accuracy. This combination promotes models that are consistently more robust and that provide well-calibrated estimates of class membership probabilities. We demonstrate the benefits of NoisyMix on a range of benchmark datasets, including ImageNet-C, ImageNet-R, and ImageNet-P. Moreover, we provide theory to understand implicit regularization and robustness of NoisyMix.


FedSpace: An Efficient Federated Learning Framework at Satellites and Ground Stations.

Jinhyun So, Kevin Hsieh, Behnaz Arzani, Shadi Noghabi, Salman Avestimehr, Ranveer Chandra

Abstract: Large-scale deployments of low Earth orbit (LEO) satellites collect massive amount of Earth imageries and sensor data, which can empower machine learning (ML) to address global challenges such as real-time disaster navigation and mitigation. However, it is often infeasible to download all the high-resolution images and train these ML models on the ground because of limited downlink bandwidth, sparse connectivity, and regularization constraints on the imagery resolution. To address these challenges, we leverage Federated Learning (FL), where ground stations and satellites collaboratively train a global ML model without sharing the captured images on the satellites. We show fundamental challenges in applying existing FL algorithms among satellites and ground stations, and we formulate an optimization problem which captures a unique trade-off between staleness and idleness. We propose a novel FL framework, named FedSpace, which dynamically schedules model aggregation based on the deterministic and time-varying connectivity according to satellite orbits. Extensive numerical evaluations based on real-world satellite images and satellite networks show that FedSpace reduces the training time by 1.7 days (38.6%) over the state-of-the-art FL algorithms.


Robust Estimation for Nonparametric Families via Generative Adversarial Networks.

Banghua Zhu, Jiantao Jiao, Michael I. Jordan

Abstract: We provide a general framework for designing Generative Adversarial Networks (GANs) to solve high dimensional robust statistics problems, which aim at estimating unknown parameter of the true distribution given adversarially corrupted samples. Prior work focus on the problem of robust mean and covariance estimation when the true distribution lies in the family of Gaussian distributions or elliptical distributions, and analyze depth or scoring rule based GAN losses for the problem. Our work extend these to robust mean estimation, second moment estimation, and robust linear regression when the true distribution only has bounded Orlicz norms, which includes the broad family of sub-Gaussian, sub-Exponential and bounded moment distributions. We also provide a different set of sufficient conditions for the GAN loss to work: we only require its induced distance function to be a cumulative density function of some light-tailed distribution, which is easily satisfied by neural networks with sigmoid activation. In terms of techniques, our proposed GAN losses can be viewed as a smoothed and generalized Kolmogorov-Smirnov distance, which overcomes the computational intractability of the original Kolmogorov-Smirnov distance used in the prior work.


Global Optimization Networks.

Sen Zhao, Erez Louidor, Olexander Mangylov, Maya Gupta

Abstract: We consider the problem of estimating a good maximizer of a black-box function given noisy examples. To solve such problems, we propose to fit a new type of function which we call a global optimization network (GON), defined as any composition of an invertible function and a unimodal function, whose unique global maximizer can be inferred in $\mathcal{O}(D)$ time. In this paper, we show how to construct invertible and unimodal functions by using linear inequality constraints on lattice models. We also extend to \emph{conditional} GONs that find a global maximizer conditioned on specified inputs of other dimensions. Experiments show the GON maximizers are statistically significantly better predictions than those produced by convex fits, GPR, or DNNs, and are more reasonable predictions for real-world problems.


Fenrir: Physics-Enhanced Regression for Initial Value Problems.

Filip Tronarp, Nathanael Bosch, Philipp Hennig

Abstract: We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyperparameter estimation in Gauss--Markov regression, which tends to be considerably easier. The method's relation and benefits in comparison to classical numerical integration and gradient matching approaches is elucidated. In particular, the method can, in contrast to gradient matching, handle partial observations, and has certain routes for escaping local optima not available to classical numerical integration. Experimental results demonstrate that the method is on par or moderately better than competing approaches.


Gradient estimators for normalising flows.

Piotr Bialas, Piotr Korcyl, Tomasz Stebel

Abstract: Recently a machine learning approach to Monte-Carlo simulations called Neural Markov Chain Monte-Carlo (NMCMC) is gaining traction. In its most popular form it uses the neural networks to construct normalizing flows which are then trained to approximate the desired target distribution. As this distribution is usually defined via a Hamiltonian or action, the standard learning algorithm requires estimation of the action gradient with respect to the fields. In this contribution we present another gradient estimator (and the corresponding [PyTorch implementation) that avoids this calculation, thus potentially speeding up training for models with more complicated actions. We also study the statistical properties of several gradient estimators and show that our formulation leads to better training results.


Generative Flow Networks for Discrete Probabilistic Modeling.

Dinghuai Zhang, Nikolay Malkin, Zhen Liu, Alexandra Volokhova, Aaron Courville, Yoshua Bengio

Abstract: We present energy-based generative flow networks (EB-GFN), a novel probabilistic modeling algorithm for high-dimensional discrete data. Building upon the theory of generative flow networks (GFlowNets), we model the generation process by a stochastic data construction policy and thus amortize expensive MCMC exploration into a fixed number of actions sampled from a GFlowNet. We show how GFlowNets can approximately perform large-block Gibbs sampling to mix between modes. We propose a framework to jointly train a GFlowNet with an energy function, so that the GFlowNet learns to sample from the energy distribution, while the energy learns with an approximate MLE objective with negative samples from the GFlowNet. We demonstrate EB-GFN's effectiveness on various probabilistic modeling tasks.


Deep Hierarchy in Bandits.

Joey Hong, Branislav Kveton, Sumeet Katariya, Manzil Zaheer, Mohammad Ghavamzadeh

Abstract: Mean rewards of actions are often correlated. The form of these correlations may be complex and unknown a priori, such as the preferences of a user for recommended products and their categories. To maximize statistical efficiency, it is important to leverage these correlations when learning. We formulate a bandit variant of this problem where the correlations of mean action rewards are represented by a hierarchical Bayesian model with latent variables. Since the hierarchy can have multiple layers, we call it deep. We propose a hierarchical Thompson sampling algorithm (HierTS) for this problem, and show how to implement it efficiently for Gaussian hierarchies. The efficient implementation is possible due to a novel exact hierarchical representation of the posterior, which itself is of independent interest. We use this exact posterior to analyze the Bayes regret of HierTS in Gaussian bandits. Our analysis reflects the structure of the problem, that the regret decreases with the prior width, and also shows that hierarchies reduce the regret by non-constant factors in the number of actions. We confirm these theoretical findings empirically, in both synthetic and real-world experiments.


Fast and explainable clustering based on sorting.

Abstract: We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The algorithm is controlled by two scalar parameters, namely a distance parameter for the aggregation and another parameter controlling the minimal cluster size. Extensive experiments are conducted to give a comprehensive evaluation of the clustering performance on synthetic and real-world datasets, with various cluster shapes and low to high feature dimensionality. Our experiments demonstrate that CLASSIX competes with state-of-the-art clustering algorithms. The algorithm has linear space complexity and achieves near linear time complexity on a wide range of problems. Its inherent simplicity allows for the generation of intuitive explanations of the computed clusters.


Minimax rate of consistency for linear models with missing values.

Alexis Ayme (LPSM (UMR\_8001)), Claire Boyer (LPSM (UMR\_8001), MOKAPLAN), Aymeric Dieuleveut (CMAP), Erwan Scornet (CMAP)

Abstract: Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually prevents us from running standard learning algorithms. In this paper, we focus on the extensively-studied linear models, but in presence of missing values, which turns out to be quite a challenging task. Indeed, the Bayes rule can be decomposed as a sum of predictors corresponding to each missing pattern. This eventually requires to solve a number of learning tasks, exponential in the number of input features, which makes predictions impossible for current real-world datasets. First, we propose a rigorous setting to analyze a least-square type estimator and establish a bound on the excess risk which increases exponentially in the dimension. Consequently, we leverage the missing data distribution to propose a new algorithm, andderive associated adaptive risk bounds that turn out to be minimax optimal. Numerical experiments highlight the benefits of our method compared to state-of-the-art algorithms used for predictions with missing values.


Byzantine-Robust Decentralized Learning via Self-Centered Clipping.

Lie He, Sai Praneeth Karimireddy, Martin Jaggi

Abstract: In this paper, we study the challenging task of Byzantine-robust decentralized training on arbitrary communication graphs. Unlike federated learning where workers communicate through a server, workers in the decentralized environment can only talk to their neighbors, making it harder to reach consensus. We identify a novel dissensus attack in which few malicious nodes can take advantage of information bottlenecks in the topology to poison the collaboration. To address these issues, we propose a Self-Centered Clipping (SCClip) algorithm for Byzantine-robust consensus and optimization, which is the first to provably converge to a $O(\delta_{\max}\zeta^2/\gamma^2)$ neighborhood of the stationary point for non-convex objectives under standard assumptions. Finally, we demonstrate the encouraging empirical performance of SCClip under a large number of attacks.


Doubly Robust Off-Policy Evaluation for Ranking Policies under the Cascade Behavior Model.

Haruka Kiyohara, Yuta Saito, Tatsuya Matsuhiro, Yusuke Narita, Nobuyuki Shimizu, Yasuo Yamamoto

Abstract: In real-world recommender systems and search engines, optimizing ranking decisions to present a ranked list of relevant items is critical. Off-policy evaluation (OPE) for ranking policies is thus gaining a growing interest because it enables performance estimation of new ranking policies using only logged data. Although OPE in contextual bandits has been studied extensively, its naive application to the ranking setting faces a critical variance issue due to the huge item space. To tackle this problem, previous studies introduce some assumptions on user behavior to make the combinatorial item space tractable. However, an unrealistic assumption may, in turn, cause serious bias. Therefore, appropriately controlling the bias-variance tradeoff by imposing a reasonable assumption is the key for success in OPE of ranking policies. To achieve a well-balanced bias-variance tradeoff, we propose the Cascade Doubly Robust estimator building on the cascade assumption, which assumes that a user interacts with items sequentially from the top position in a ranking. We show that the proposed estimator is unbiased in more cases compared to existing estimators that make stronger assumptions. Furthermore, compared to a previous estimator based on the same cascade assumption, the proposed estimator reduces the variance by leveraging a control variate. Comprehensive experiments on both synthetic and real-world data demonstrate that our estimator leads to more accurate OPE than existing estimators in a variety of settings.


Unified theory of atom-centered representations and graph convolutional machine-learning schemes.

Jigyasa Nigam, Guillaume Fraux, Michele Ceriotti

Abstract: Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, that are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), that are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes, that gather information on the relationship between neighboring atoms using graph-convolutional (or message-passing) ideas, cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and form the basis to systematize our understanding of both atom-centered and graph-convolutional machine-learning schemes.


The RoyalFlush System of Speech Recognition for M2MeT Challenge.

Shuaishuai Ye, Peiyao Wang, Shunfei Chen, Xinhui Hu, Xinkang Xu

Abstract: This paper describes our RoyalFlush system for the track of multi-speaker automatic speech recognition (ASR) in the M2MeT challenge. We adopted the serialized output training (SOT) based multi-speakers ASR system with large-scale simulation data. Firstly, we investigated a set of front-end methods, including multi-channel weighted predicted error (WPE), beamforming, speech separation, speech enhancement and so on, to process training, validation and test sets. But we only selected WPE and beamforming as our frontend methods according to their experimental results. Secondly, we made great efforts in the data augmentation for multi-speaker ASR, mainly including adding noise and reverberation, overlapped speech simulation, multi-channel speech simulation, speed perturbation, front-end processing, and so on, which brought us a great performance improvement. Finally, in order to make full use of the performance complementary of different model architecture, we trained the standard conformer based joint CTC/Attention (Conformer) and U2++ ASR model with a bidirectional attention decoder, a modification of Conformer, to fuse their results. Comparing with the official baseline system, our system got a 12.22% absolute Character Error Rate (CER) reduction on the validation set and 12.11% on the test set.


On Manifold Hypothesis: Hypersurface Submanifold Embedding Using Osculating Hyperspheres.

Benyamin Ghojogh, Fakhri Karray, Mark Crowley

Abstract: Consider a set of $n$ data points in the Euclidean space $\mathbb{R}^d$. This set is called dataset in machine learning and data science. Manifold hypothesis states that the dataset lies on a low-dimensional submanifold with high probability. All dimensionality reduction and manifold learning methods have the assumption of manifold hypothesis. In this paper, we show that the dataset lies on an embedded hypersurface submanifold which is locally $(d-1)$-dimensional. Hence, we show that the manifold hypothesis holds at least for the embedding dimensionality $d-1$. Using an induction in a pyramid structure, we also extend the embedding dimensionality to lower embedding dimensionalities to show the validity of manifold hypothesis for embedding dimensionalities $\{1, 2, \dots, d-1\}$. For embedding the hypersurface, we first construct the $d$ nearest neighbors graph for data. For every point, we fit an osculating hypersphere $S^{d-1}$ using its neighbors where this hypersphere is osculating to a hypothetical hypersurface. Then, using surgery theory, we apply surgery on the osculating hyperspheres to obtain $n$ hyper-caps. We connect the hyper-caps to one another using partial hyper-cylinders. By connecting all parts, the embedded hypersurface is obtained as the disjoint union of these elements. We discuss the geometrical characteristics of the embedded hypersurface, such as having boundary, its topology, smoothness, boundedness, orientability, compactness, and injectivity. Some discussion are also provided for the linearity and structure of data. This paper is the intersection of several fields of science including machine learning, differential geometry, and algebraic topology.


Efficient learning of hidden state LTI state space models of unknown order.

Abstract: The aim of this paper is to address two related estimation problems arising in the setup of hidden state linear time invariant (LTI) state space systems when the dimension of the hidden state is unknown. Namely, the estimation of any finite number of the system's Markov parameters and the estimation of a minimal realization for the system, both from the partial observation of a single trajectory. For both problems, we provide statistical guarantees in the form of various estimation error upper bounds, $\rank$ recovery conditions, and sample complexity estimates.  Specifically, we first show that the low $\rank$ solution of the Hankel penalized least square estimator satisfies an estimation error in $S_p$-norms for $p \in [1,2]$ that captures the effect of the system order better than the existing operator norm upper bound for the simple least square. We then provide a stability analysis for an estimation procedure based on a variant of the Ho-Kalman algorithm that improves both the dependence on the dimension and the least singular value of the Hankel matrix of the Markov parameters. Finally, we propose an estimation algorithm for the minimal realization that uses both the Hankel penalized least square estimator and the Ho-Kalman based estimation procedure and guarantees with high probability that we recover the correct order of the system and satisfies a new fast rate in the $S_2$-norm with a polynomial reduction in the dependence on the dimension and other parameters of the problem.


Non-Vacuous Generalisation Bounds for Shallow Neural Networks.

Abstract: We focus on a specific class of shallow neural networks with a single hidden layer, namely those with $L_2$-normalised data and either a sigmoid-shaped Gaussian error function ("erf") activation or a Gaussian Error Linear Unit (GELU) activation. For these networks, we derive new generalisation bounds through the PAC-Bayesian theory; unlike most existing such bounds they apply to neural networks with deterministic rather than randomised parameters. Our bounds are empirically non-vacuous when the network is trained with vanilla stochastic gradient descent on MNIST and Fashion-MNIST.


Selection in the Presence of Implicit Bias: The Advantage of Intersectional Constraints.

Anay Mehrotra, Bary S. R. Pradelski, Nisheeth K. Vishnoi

Abstract: In selection processes such as hiring, promotion, and college admissions, implicit bias toward socially-salient attributes such as race, gender, or sexual orientation of candidates is known to produce persistent inequality and reduce aggregate utility for the decision maker. Interventions such as the Rooney Rule and its generalizations, which require the decision maker to select at least a specified number of individuals from each affected group, have been proposed to mitigate the adverse effects of implicit bias in selection. Recent works have established that such lower-bound constraints can be very effective in improving aggregate utility in the case when each individual belongs to at most one affected group. However, in several settings, individuals may belong to multiple affected groups and, consequently, face more extreme implicit bias due to this intersectionality. We consider independently drawn utilities and show that, in the intersectional case, the aforementioned non-intersectional constraints can only recover part of the total utility achievable in the absence of implicit bias. On the other hand, we show that if one includes appropriate lower-bound constraints on the intersections, almost all the utility achievable in the absence of implicit bias can be recovered. Thus, intersectional constraints can offer a significant advantage over a reductionist dimension-by-dimension non-intersectional approach to reducing inequality.


Equality Is Not Equity: Proportional Fairness in Federated Learning.

Guojun Zhang, Saber Malekmohammadi, Xi Chen, Yaoliang Yu

Abstract: Ensuring fairness of machine learning (ML) algorithms is becoming an increasingly important mission for ML service providers. This is even more critical and challenging in the federated learning (FL) scenario, given a large number of diverse participating clients. Simply mandating equality across clients could lead to many undesirable consequences, potentially discouraging high-performing clients and resulting in sub-optimal overall performance. In order to achieve better equity rather than equality, in this work, we introduce and study proportional fairness (PF) in FL, which has a deep connection with game theory. By viewing FL from a cooperative game perspective, where the players (clients) collaboratively learn a good model, we formulate PF as Nash bargaining solutions. Based on this concept, we propose PropFair, a novel and easy-to-implement algorithm for effectively finding PF solutions, and we prove its convergence properties. We illustrate through experiments that PropFair consistently improves the worst-case and the overall performances simultaneously over state-of-the-art fair FL algorithms for a wide array of vision and language datasets, thus achieving better equity.


Log-Euclidean Signatures for Intrinsic Distances Between Unaligned Datasets.

Tal Shnitzer, Mikhail Yurochkin, Kristjan Greenewald, Justin Solomon

Abstract: The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning to compare the intrinsic geometric structures of different datasets by comparing their diffusion operators, symmetric positive-definite (SPD) matrices that relate to approximations of the continuous Laplace-Beltrami operator from discrete samples. Existing methods typically compare such operators in a pointwise manner or assume known data alignment. Instead, we exploit the Riemannian geometry of SPD matrices to compare these operators and define a new theoretically-motivated distance based on a lower bound of the log-Euclidean metric. Our framework facilitates comparison of data manifolds expressed in datasets with different sizes, numbers of features, and measurement modalities. Our log-Euclidean signature (LES) distance recovers meaningful structural differences, outperforming competing methods in various application domains.


Variational Nearest Neighbor Gaussian Processes.

Luhuan Wu, Geoff Pleiss, John Cunningham

Abstract: Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix. We propose variational nearest neighbor Gaussian process (VNNGP), which introduces a prior that only retains correlations within K nearest-neighboring observations, thereby inducing sparse precision structure. Using the variational framework, VNNGP's objective can be factorized over both observations and inducing points, enabling stochastic optimization with a time complexity of O($K^3$). Hence, we can arbitrarily scale the inducing point size, even to the point of putting inducing points at every observed location. We compare VNNGP to other scalable GPs through various experiments, and demonstrate that VNNGP (1) can dramatically outperform low-rank methods, and (2) is less prone to overfitting than other nearest neighbor methods.


Sequential Learning of the Topological Ordering for the Linear Non-Gaussian Acyclic Model with Parametric Noise.

Gabriel Ruiz, Oscar Hernan Madrid Padilla, Qing Zhou

Abstract: Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions, it is sometimes possible to identify an exact causal Directed Acyclic Graph (DAG), as opposed to a Markov equivalence class of graphs that gives ambiguity of causal directions. The focus of this paper is on one such case: a linear structural equation model with non-Gaussian noise, a model known as the Linear Non-Gaussian Acyclic Model (LiNGAM). Given a specified parametric noise model, we develop a novel sequential approach to estimate the causal ordering of a DAG. At each step of the procedure, only simple likelihood ratio scores are calculated on regression residuals to decide the next node to append to the current partial ordering. Under mild assumptions, the population version of our procedure provably identifies a true ordering of the underlying causal DAG. We provide extensive numerical evidence to demonstrate that our sequential procedure is scalable to cases with possibly thousands of nodes and works well for high-dimensional data. We also conduct an application to a single-cell gene expression dataset to demonstrate our estimation procedure.


Near-Optimal Learning of Extensive-Form Games with Imperfect Information.

Abstract: This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only $\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$ episodes of play to find an $\varepsilon$-approximate Nash equilibrium in two-player zero-sum games, where $X,Y$ are the number of information sets and $A,B$ are the number of actions for the two players. This improves upon the best known sample complexity of $\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$ by a factor of $\widetilde{\mathcal{O}}(\max\{X, Y\})$, and matches the information-theoretic lower bound up to logarithmic factors. We achieve this sample complexity by two new algorithms: Balanced Online Mirror Descent, and Balanced Counterfactual Regret Minimization. Both algorithms rely on novel approaches of integrating \emph{balanced exploration policies} into their classical counterparts. We also extend our results to learning Coarse Correlated Equilibria in multi-player general-sum games.


Multiclass learning with margin: exponential rates with no bias-variance trade-off.

Stefano Vigogna, Giacomo Meanti, Ernesto De Vito, Lorenzo Rosasco

Abstract: We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without any bias-variance trade-off. Different convergence rates can be obtained in correspondence of different margin assumptions. With a self-contained and instructive analysis we are able to generalize known results from the binary to the multiclass setting.


PageRank algorithm for Directed Hypergraph.

Abstract: During the last two decades, we easilly see that the World Wide Web's link structure is modeled as the directed graph. In this paper, we will model the World Wide Web's link structure as the directed hypergraph. Moreover, we will develop the PageRank algorithm for this directed hypergraph. Due to the lack of the World Wide Web directed hypergraph datasets, we will apply the PageRank algorithm to the metabolic network which is the directed hypergraph itself. The experiments show that our novel PageRank algorithm is successfully applied to this metabolic network.


Sharpe Ratio Analysis in High Dimensions: Residual-Based Nodewise Regression in Factor Models.

Mehmet Caner, Marcelo Medeiros, Gabriel Vasconcelos

Abstract: We provide a new theory for nodewise regression when the residuals from a fitted factor model are used. We apply our results to the analysis of the consistency of Sharpe ratio estimators when there are many assets in a portfolio. We allow for an increasing number of assets as well as time observations of the portfolio. Since the nodewise regression is not feasible due to the unknown nature of idiosyncratic errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors which is consistent even when number of assets, p, exceeds the time span of the portfolio, n. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors and p>n. We show that: (1) with p>n, the Sharpe ratio estimators are consistent in global minimum-variance and mean-variance portfolios; and (2) with p>n, the maximum Sharpe ratio estimator is consistent when the portfolio weights sum to one; and (3) with p<<n, the maximum-out-of-sample Sharpe ratio estimator is consistent.


Optimality and Stability in Non-Convex Smooth Games.

Guojun Zhang, Pascal Poupart, Yaoliang Yu

Abstract: Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an intriguing research challenge how local optimal points are defined and which algorithm can converge to such points. An interesting concept is known as the local minimax point, which strongly correlates with the widely-known gradient descent ascent algorithm. This paper aims to provide a comprehensive analysis of local minimax points, such as their relation with other solution concepts and their optimality conditions. We find that local saddle points can be regarded as a special type of local minimax points, called uniformly local minimax points, under mild continuity assumptions. In (non-convex) quadratic games, we show that local minimax points are (in some sense) equivalent to global minimax points. Finally, we study the stability of gradient algorithms near local minimax points. Although gradient algorithms can converge to local/global minimax points in the non-degenerate case, they would often fail in general cases. This implies the necessity of either novel algorithms or concepts beyond saddle points and minimax points in non-convex smooth games.


Assessing External Validity Over Worst-case Subpopulations.

Abstract: Study populations are typically sampled from limited points in space and time, and marginalized groups are underrepresented. To assess the external validity of randomized and observational studies, we propose and evaluate the worst-case treatment effect (WTE) across all subpopulations of a given size, which guarantees positive findings remain valid over subpopulations. We develop a semiparametrically efficient estimator for the WTE that analyzes the external validity of the augmented inverse propensity weighted estimator for the average treatment effect. Our cross-fitting procedure leverages flexible nonparametric and machine learning-based estimates of nuisance parameters and is a regular root-$n$ estimator even when nuisance estimates converge more slowly. On real examples where external validity is of core concern, our proposed framework guards against brittle findings that are invalidated by unanticipated population shifts.


Accounting for Unobserved Confounding in Domain Generalization.

Abstract: This paper investigates the problem of learning robust, generalizable prediction models from a combination of multiple datasets and qualitative assumptions about the underlying data-generating model. Part of the challenge of learning robust models lies in the influence of unobserved confounders that void many of the invariances and principles of minimum error presently used for this problem. Our approach is to define a different invariance property of causal solutions in the presence of unobserved confounders which, through a relaxation of this invariance, can be connected with an explicit distributionally robust optimization problem over a set of affine combination of data distributions. Concretely, our objective takes the form of a standard loss, plus a regularization term that encourages partial equality of error derivatives with respect to model parameters. We demonstrate the empirical performance of our approach on healthcare data from different modalities, including image, speech and tabular data.


Directed hypergraph neural network.

Abstract: To deal with irregular data structure, graph convolution neural networks have been developed by a lot of data scientists. However, data scientists just have concentrated primarily on developing deep neural network method for un-directed graph. In this paper, we will present the novel neural network method for directed hypergraph. In the other words, we will develop not only the novel directed hypergraph neural network method but also the novel directed hypergraph based semi-supervised learning method. These methods are employed to solve the node classification task. The two datasets that are used in the experiments are the cora and the citeseer datasets. Among the classic directed graph based semi-supervised learning method, the novel directed hypergraph based semi-supervised learning method, the novel directed hypergraph neural network method that are utilized to solve this node classification task, we recognize that the novel directed hypergraph neural network achieves the highest accuracies.


Noise-robust classification with hypergraph neural network.

Nguyen Trinh Vu Dang, Loc Tran, Linh Tran

Abstract: This paper presents a novel version of the hypergraph neural network method. This method is utilized to solve the noisy label learning problem. First, we apply the PCA dimensional reduction technique to the feature matrices of the image datasets in order to reduce the "noise" and the redundant features in the feature matrices of the image datasets and to reduce the runtime constructing the hypergraph of the hypergraph neural network method. Then, the classic graph-based semi-supervised learning method, the classic hypergraph based semi-supervised learning method, the graph neural network, the hypergraph neural network, and our proposed hypergraph neural network are employed to solve the noisy label learning problem. The accuracies of these five methods are evaluated and compared. Experimental results show that the hypergraph neural network methods achieve the best performance when the noise level increases. Moreover, the hypergraph neural network methods are at least as good as the graph neural network.


Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron: The Haar Orthogonal Case.

Abstract: Free Probability Theory (FPT) provides rich knowledge for handling mathematical difficulties caused by random matrices that appear in research related to deep neural networks (DNNs), such as the dynamical isometry, Fisher information matrix, and training dynamics. FPT suits these researches because the DNN's parameter-Jacobian and input-Jacobian are polynomials of layerwise Jacobians. However, the critical assumption of asymptotic freenss of the layerwise Jacobian has not been proven completely so far. The asymptotic freeness assumption plays a fundamental role when propagating spectral distributions through the layers. Haar distributed orthogonal matrices are essential for achieving dynamical isometry. In this work, we prove asymptotic freeness of layerwise Jacobians of multilayer perceptron (MLP) in this case. A key of the proof is an invariance of the MLP. Considering the orthogonal matrices that fix the hidden units in each layer, we replace each layer's parameter matrix with itself multiplied by the orthogonal matrix, and then the MLP does not change. Furthermore, if the original weights are Haar orthogonal, the Jacobian is also unchanged by this replacement. Lastly, we can replace each weight with a Haar orthogonal random matrix independent of the Jacobian of the activation function using this key fact.


Sampling Permutations for Shapley Value Estimation.

Rory Mitchell, Joshua Cooper, Eibe Frank, Geoffrey Holmes

Abstract: Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the computation of Shapley values can be expressed as a summation over a set of permutations, a common approach is to sample a subset of these permutations for approximation. Unfortunately, standard Monte Carlo sampling methods can exhibit slow convergence, and more sophisticated quasi-Monte Carlo methods have not yet been applied to the space of permutations. To address this, we investigate new approaches based on two classes of approximation methods and compare them empirically. First, we demonstrate quadrature techniques in a RKHS containing functions of permutations, using the Mallows kernel in combination with kernel herding and sequential Bayesian quadrature. The RKHS perspective also leads to quasi-Monte Carlo type error bounds, with a tractable discrepancy measure defined on permutations. Second, we exploit connections between the hypersphere $\mathbb{S}^{d-2}$ and permutations to create practical algorithms for generating permutation samples with good properties. Experiments show the above techniques provide significant improvements for Shapley value estimates over existing methods, converging to a smaller RMSE in the same number of model evaluations.


Neural graphical modelling in continuous-time: consistency guarantees and algorithms.

Alexis Bellot, Kim Branson, Mihaela van der Schaar

Abstract: The discovery of structure from time series data is a key problem in fields of study working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define dependencies in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider score-based structure learning for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, least squares optimization with adaptive regularization schemes consistently recovers directed graphs of local independencies in systems of stochastic differential equations. Using this insight, we propose a score-based learning algorithm based on penalized Neural Ordinary Differential Equations (modelling the mean process) that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to outperform the state of the art across a range of dynamical systems.


A Stochastic Alternating Balance $k$-Means Algorithm for Fair Clustering.

Abstract: In the application of data clustering to human-centric decision-making systems, such as loan applications and advertisement recommendations, the clustering outcome might discriminate against people across different demographic groups, leading to unfairness. A natural conflict occurs between the cost of clustering (in terms of distance to cluster centers) and the balance representation of all demographic groups across the clusters, leading to a bi-objective optimization problem that is nonconvex and nonsmooth. To determine the complete trade-off between these two competing goals, we design a novel stochastic alternating balance fair $k$-means (SAfairKM) algorithm, which consists of alternating classical mini-batch $k$-means updates and group swap updates. The number of $k$-means updates and the number of swap updates essentially parameterize the weight put on optimizing each objective function. Our numerical experiments show that the proposed SAfairKM algorithm is robust and computationally efficient in constructing well-spread and high-quality Pareto fronts both on synthetic and real datasets.


Hierarchical Bayesian Mixture Models for Time Series Using Context Trees as State Space Partitions.

Ioannis Papageorgiou, Ioannis Kontoyiannis

Abstract: A general Bayesian framework is introduced for mixture modelling and inference with real-valued time series. At the top level, the state space is partitioned via the choice of a discrete context tree, so that the resulting partition depends on the values of some of the most recent samples. At the bottom level, a different model is associated with each region of the partition. This defines a very rich and flexible class of mixture models, for which we provide algorithms that allow for efficient, exact Bayesian inference. In particular, we show that the maximum a posteriori probability (MAP) model (including the relevant MAP context tree partition) can be precisely identified, along with its exact posterior probability. The utility of this general framework is illustrated in detail when a different autoregressive (AR) model is used in each state-space region, resulting in a mixture-of-AR model class. The performance of the associated algorithmic tools is demonstrated in the problems of model selection and forecasting on both simulated and real-world data, where they are found to provide results as good or better than state-of-the-art methods.


A Reputation Game Simulation: Emergent Social Phenomena from Information Theory.

Torsten Enßlin, Viktoria Kainz, Céline Bœhm

Abstract: Reputation is a central element of social communications, be it with human or artificial intelligence (AI), and as such can be the primary target of malicious communication strategies. There is already a vast amount of literature on trust networks addressing this issue and proposing ways to simulate these networks dynamics using Bayesian principles and involving Theory of Mind models. The main issue for these simulations is usually the amount of information that can be stored and is usually solved by discretising variables and using hard thresholds. Here we propose a novel approach to the way information is updated that accounts for knowledge uncertainty and is closer to reality. In our game, agents use information compression techniques to capture their complex environment and store it in their finite memories. The loss of information that results from this leads to emergent phenomena, such as echo chambers, self-deception, deception symbiosis, and freezing of group opinions. Various malicious strategies of agents are studied for their impact on group sociology, like sycophancy, egocentricity, pathological lying, and aggressiveness. Even though our modeling could be made more complex, our set-up can already provide insights into social interactions and can be used to investigate the effects of various communication strategies and find ways to counteract malicious ones. Eventually this work should help to safeguard the design of non-abusive AI systems.


Contrastive Mixture of Posteriors for Counterfactual Inference, Data Integration and Fairness.

Adam Foster, Árpi Vezér, Craig A Glastonbury, Páidí Creed, Sam Abujudeh, Aaron Sim

Abstract: Learning meaningful representations of data that can address challenges such as batch effect correction and counterfactual inference is a central problem in many domains including computational biology. Adopting a Conditional VAE framework, we show that marginal independence between the representation and a condition variable plays a key role in both of these challenges. We propose the Contrastive Mixture of Posteriors (CoMP) method that uses a novel misalignment penalty defined in terms of mixtures of the variational posteriors to enforce this independence in latent space. We show that CoMP has attractive theoretical properties compared to previous approaches and we prove counterfactual identifiability of CoMP under additional assumptions. We demonstrate state of the art performance on a set of challenging tasks including aligning human tumour samples with cancer cell-lines, predicting transcriptome-level perturbation responses, and batch correction on single-cell RNA sequencing data. We also find parallels to fair representation learning and demonstrate that CoMP is competitive on a common task in the field.


Adaptive Clustering and Personalization in Multi-Agent Stochastic Linear Bandits.

Avishek Ghosh, Abishek Sankararaman, Kannan Ramchandran

Abstract: We consider the problem of minimizing regret in an $N$ agent heterogeneous stochastic linear bandits framework, where the agents (users) are similar but not all identical. We model user heterogeneity using two popularly used ideas in practice; (i) A clustering framework where users are partitioned into groups with users in the same group being identical to each other, but different across groups, and (ii) a personalization framework where no two users are necessarily identical, but a user's parameters are close to that of the population average. In the clustered users' setup, we propose a novel algorithm, based on successive refinement of cluster identities and regret minimization. We show that, for any agent, the regret scales as $\mathcal{O}(\sqrt{T/N})$, if the agent is in a `well separated' cluster, or scales as $\mathcal{O}(T^{\frac{1}{2} + \varepsilon}/(N)^{\frac{1}{2} -\varepsilon})$ if its cluster is not well separated, where $\varepsilon$ is positive and arbitrarily close to $0$. Our algorithm is adaptive to the cluster separation, and is parameter free -- it does not need to know the number of clusters, separation and cluster size, yet the regret guarantee adapts to the inherent complexity. In the personalization framework, we introduce a natural algorithm where, the personal bandit instances are initialized with the estimates of the global average model. We show that, an agent $i$ whose parameter deviates from the population average by $\epsilon_i$, attains a regret scaling of $\widetilde{O}(\epsilon_i\sqrt{T})$. This demonstrates that if the user representations are close (small $\epsilon_i)$, the resulting regret is low, and vice-versa. The results are empirically validated and we observe superior performance of our adaptive algorithms over non-adaptive baselines.


Multirate Training of Neural Networks.

Abstract: We propose multirate training of neural networks: partitioning neural network parameters into "fast" and "slow" parts which are trained on different time scales. By choosing appropriate partitionings we can obtain substantial computational speed-up for transfer learning tasks. We show for applications in vision and NLP that we can fine-tune deep neural networks in almost half the time, without reducing the generalization performance of the resulting models. We analyze the convergence properties of our multirate scheme and draw a comparison with vanilla SGD. We also discuss splitting choices for the neural network parameters which could enhance generalization performance when neural networks are trained from scratch. A multirate approach can be used to learn different features present in the data and as a form of regularization. Our paper unlocks the potential of using multirate techniques for neural network training and provides several starting points for future work in this area.


What can linear interpolation of neural network loss landscapes tell us?.

Abstract: Studying neural network loss landscapes provides insights into the nature of the underlying optimization problems. Unfortunately, loss landscapes are notoriously difficult to visualize in a human-comprehensible fashion. One common way to address this problem is to plot linear slices of the landscape, for example from the initial state of the network to the final state after optimization. On the basis of this analysis, prior work has drawn broader conclusions about the difficulty of the optimization problem. In this paper, we put inferences of this kind to the test, systematically evaluating how linear interpolation and final performance vary when altering the data, choice of initialization, and other optimizer and architecture design choices. Further, we use linear interpolation to study the role played by individual layers and substructures of the network. We find that certain layers are more sensitive to the choice of initialization, but that the shape of the linear path is not indicative of the changes in test accuracy of the model. Our results cast doubt on the broader intuition that the presence or absence of barriers when interpolating necessarily relates to the success of optimization.


How many degrees of freedom do we need to train deep networks: a loss landscape perspective.

Brett W. Larsen, Stanislav Fort, Nic Becker, Surya Ganguli

Abstract: A variety of recent works, spanning pruning, lottery tickets, and training within random subspaces, have shown that deep neural networks can be trained using far fewer degrees of freedom than the total number of parameters. We analyze this phenomenon for random subspaces by first examining the success probability of hitting a training loss sub-level set when training within a random subspace of a given training dimensionality. We find a sharp phase transition in the success probability from $0$ to $1$ as the training dimension surpasses a threshold. This threshold training dimension increases as the desired final loss decreases, but decreases as the initial loss decreases. We then theoretically explain the origin of this phase transition, and its dependence on initialization and final desired loss, in terms of properties of the high-dimensional geometry of the loss landscape. In particular, we show via Gordon's escape theorem, that the training dimension plus the Gaussian width of the desired loss sub-level set, projected onto a unit sphere surrounding the initialization, must exceed the total number of parameters for the success probability to be large. In several architectures and datasets, we measure the threshold training dimension as a function of initialization and demonstrate that it is a small fraction of the total parameters, implying by our theory that successful training with so few dimensions is possible precisely because the Gaussian width of low loss sub-level sets is very large. Moreover, we compare this threshold training dimension to more sophisticated ways of reducing training degrees of freedom, including lottery tickets as well as a new, analogous method: lottery subspaces. Code is available at https://github.com/ganguli-lab/degrees-of-freedom.


Double Machine Learning for Partially Linear Mixed-Effects Models with Repeated Measurements.

Abstract: Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed-effects model for repeated measurements. Using machine learning algorithms allows us to incorporate complex interaction structures and high-dimensional variables. We employ double machine learning to cope with the nonparametric part of the partially linear mixed-effects model: the nonlinear variables are regressed out nonparametrically from both the linear variables and the response. This adjustment can be performed with any machine learning algorithm, for instance random forests, which allows to take complex interaction terms and nonsmooth structures into account. The adjusted variables satisfy a linear mixed-effects model, where the linear coefficient can be estimated with standard linear mixed-effects techniques. We prove that the estimated fixed effects coefficient converges at the parametric rate, is asymptotically Gaussian distributed, and semiparametrically efficient. Two simulation studies demonstrate that our method outperforms a penalized regression spline approach in terms of coverage. We also illustrate our proposed approach on a longitudinal dataset with HIV-infected individuals. Software code for our method is available in the R-package dmlalg.


Partitioning Cloud-based Microservices (via Deep Learning).

Rahul Yedida, Rahul Krishna, Anup Kalia, Tim Menzies, Jin Xiao, Maja Vukovic

Abstract: Cloud-based software has many advantages. When services are divided into many independent components, they are easier to update. Also, during peak demand, it is easier to scale cloud services (just hire more CPUs). Hence, many organizations are partitioning their monolithic enterprise applications into cloud-based microservices.  Recently there has been much work using machine learning to simplify this partitioning task. Despite much research, no single partitioning method can be recommended as generally useful. More specifically, those prior solutions are "brittle"; i.e. if they work well for one kind of goal in one dataset, then they can be sub-optimal if applied to many datasets and multiple goals.  In order to find a generally useful partitioning method, we propose DEEPLY. This new algorithm extends the CO-GCN deep learning partition generator with (a) a novel loss function and (b) some hyper-parameter optimization. As shown by our experiments, DEEPLY generally outperforms prior work (including CO-GCN, and others) across multiple datasets and goals. To the best of our knowledge, this is the first report in SE of such stable hyper-parameter optimization.  To aid reuse of this work, DEEPLY is available on-line at https://bit.ly/2WhfFlB.


The Terminating-Knockoff Filter: Fast High-Dimensional Variable Selection with False Discovery Rate Control.

Jasin Machkour, Michael Muma, Daniel P. Palomar

Abstract: We propose the Terminating-Knockoff (T-Knock) filter, a fast variable selection method for high-dimensional data. The T-Knock filter controls a user-defined target false discovery rate (FDR) while maximizing the number of selected variables. This is achieved by fusing the solutions of multiple early terminated random experiments. The experiments are conducted on a combination of the original predictors and multiple sets of randomly generated knockoff predictors. A finite sample proof based on martingale theory for the FDR control property is provided. Numerical simulations show that the FDR is controlled at the target level while allowing for a high power. We prove under mild conditions that the knockoffs can be sampled from any univariate probability distribution with existing finite expectation and variance. The computational complexity of the proposed method is derived and it is demonstrated via numerical simulations that the sequential computation time is multiple orders of magnitude lower than that of the strongest benchmark methods in sparse high-dimensional settings. The T-Knock filter outperforms state-of-the-art methods for FDR control on a simulated genome-wide association study (GWAS), while its computation time is more than two orders of magnitude lower than that of the strongest benchmark methods. An open source R package containing the implementation of the T-Knock filter is available at https://github.com/jasinmachkour/tknock.


What Happens after SGD Reaches Zero Loss? --A Mathematical Framework.

Abstract: Understanding the implicit bias of Stochastic Gradient Descent (SGD) is one of the key challenges in deep learning, especially for overparametrized models, where the local minimizers of the loss function $L$ can form a manifold. Intuitively, with a sufficiently small learning rate $\eta$, SGD tracks Gradient Descent (GD) until it gets close to such manifold, where the gradient noise prevents further convergence. In such a regime, Blanc et al. (2020) proved that SGD with label noise locally decreases a regularizer-like term, the sharpness of loss, $\mathrm{tr}[\nabla^2 L]$. The current paper gives a general framework for such analysis by adapting ideas from Katzenberger (1991). It allows in principle a complete characterization for the regularization effect of SGD around such manifold -- i.e., the "implicit bias" -- using a stochastic differential equation (SDE) describing the limiting dynamics of the parameters, which is determined jointly by the loss function and the noise covariance. This yields some new results: (1) a global analysis of the implicit bias valid for $\eta^{-2}$ steps, in contrast to the local analysis of Blanc et al. (2020) that is only valid for $\eta^{-1.6}$ steps and (2) allowing arbitrary noise covariance. As an application, we show with arbitrary large initialization, label noise SGD can always escape the kernel regime and only requires $O(\kappa\ln d)$ samples for learning an $\kappa$-sparse overparametrized linear model in $\mathbb{R}^d$ (Woodworth et al., 2020), while GD initialized in the kernel regime requires $\Omega(d)$ samples. This upper bound is minimax optimal and improves the previous $\tilde{O}(\kappa^2)$ upper bound (HaoChen et al., 2020).


Gaussian Process Sampling and Optimization with Approximate Upper and Lower Bounds.

Vu Nguyen, Marc Peter Deisenroth, Michael A. Osborne

Abstract: Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More specifically, we propose the first use of such bounds to improve Gaussian process (GP) posterior sampling and Bayesian optimization (BO). That is, we transform a GP model satisfying the given bounds, and then sample and weight functions from its posterior. To further exploit these bounds in BO settings, we present bounded entropy search (BES) to select the point gaining the most information about the underlying function, estimated by the GP samples, while satisfying the output constraints. We characterize the sample variance bounds and show that the decision made by BES is explainable. Our proposed approach is conceptually straightforward and can be used as a plug in extension to existing methods for GP posterior sampling and Bayesian optimization.


Rademacher Random Projections with Tensor Networks.

Beheshteh T. Rakhshan, Guillaume Rabusseau

Abstract: Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random projection relying on Tensor Train (TT) decomposition where each element of the core tensors is drawn from a Rademacher distribution. Our theoretical results reveal that the Gaussian low-rank tensor represented in compressed form in TT format in [30] can be replaced by a TT tensor with core elements drawn from a Rademacher distribution with the same embedding size. Experiments on synthetic data demonstrate that tensorized Rademacher RP can outperform the tensorized Gaussian RP studied in [30]. In addition, we show both theoretically and experimentally, that the tensorized RP in the Matrix Product Operator (MPO) format is not a Johnson-Lindenstrauss transform (JLT) and therefore not a well-suited random projection map


Text classification problems via BERT embedding method and graph convolutional neural network.

Abstract: This paper presents the novel way combining the BERT embedding method and the graph convolutional neural network. This combination is employed to solve the text classification problem. Initially, we apply the BERT embedding method to the texts (in the BBC news dataset and the IMDB movie reviews dataset) in order to transform all the texts to numerical vector. Then, the graph convolutional neural network will be applied to these numerical vectors to classify these texts into their ap-propriate classes/labels. Experiments show that the performance of the graph convolutional neural network model is better than the perfor-mances of the combination of the BERT embedding method with clas-sical machine learning models.


Scaling Structured Inference with Randomization.

Yao Fu, John P. Cunningham, Mirella Lapata

Abstract: Deep discrete structured models have seen considerable progress recently, but traditional inference using dynamic programming (DP) typically works with a small number of states (less than hundreds), which severely limits model capacity. At the same time, across machine learning, there is a recent trend of using randomized truncation techniques to accelerate computations involving large sums. Here, we propose a family of randomized dynamic programming (RDP) algorithms for scaling structured models to tens of thousands of latent states. Our method is widely applicable to classical DP-based inference (partition, marginal, reparameterization, entropy) and different graph structures (chains, trees, and more general hypergraphs). It is also compatible with automatic differentiation: it can be integrated with neural networks seamlessly and learned with gradient-based optimizers. Our core technique approximates the sum-product by restricting and reweighting DP on a small subset of nodes, which reduces computation by orders of magnitude. We further achieve low bias and variance via Rao-Blackwellization and importance sampling. Experiments over different graphs demonstrate the accuracy and efficiency of our approach. Furthermore, when using RDP for training a structured variational autoencoder with a scaled inference network, we achieve better test likelihood than baselines and successfully prevent posterior collapse


Modeling Advection on Directed Graphs using Mat\'ern Gaussian Processes for Traffic Flow.

Danielle C Maddix, Nadim Saad, Yuyang Wang

Abstract: The transport of traffic flow can be modeled by the advection equation. Finite difference and finite volumes methods have been used to numerically solve this hyperbolic equation on a mesh. Advection has also been modeled discretely on directed graphs using the graph advection operator [4, 18]. In this paper, we first show that we can reformulate this graph advection operator as a finite difference scheme. We then propose the Directed Graph Advection Mat\'ern Gaussian Process (DGAMGP) model that incorporates the dynamics of this graph advection operator into the kernel of a trainable Mat\'ern Gaussian Process to effectively model traffic flow and its uncertainty as an advective process on a directed graph.


Improved Random Features for Dot Product Kernels.

Jonas Wacker, Motonobu Kanagawa, Maurizio Filippone

Abstract: Dot product kernels, such as polynomial and exponential (softmax) kernels, are among the most widely used kernels in machine learning, as they enable modeling the interactions between input features, which is crucial in applications like computer vision, natural language processing, and recommender systems. We make several novel contributions for improving the efficiency of random feature approximations for dot product kernels, to make these kernels more useful in large scale learning. First, we present a generalization of existing random feature approximations for polynomial kernels, such as Rademacher and Gaussian sketches and TensorSRHT, using complex-valued random features. We show empirically that the use of complex features can significantly reduce the variances of these approximations. Second, we provide a theoretical analysis for understanding the factors affecting the efficiency of various random feature approximations, by deriving closed-form expressions for their variances. These variance formulas elucidate conditions under which certain approximations (e.g., TensorSRHT) achieve lower variances than others (e.g., Rademacher sketches), and conditions under which the use of complex features leads to lower variances than real features. Third, by using these variance formulas, which can be evaluated in practice, we develop a data-driven optimization approach to improve random feature approximations for general dot product kernels, which is also applicable to the Gaussian kernel. We describe the improvements brought by these contributions with extensive experiments on a variety of tasks and datasets.


Memory-Efficient Backpropagation through Large Linear Layers.

Daniel Bershatsky, Aleksandr Mikhalev, Alexandr Katrutsa, Julia Gusak, Daniil Merkulov, Ivan Oseledets

Abstract: In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the gradients of linear layers are computed by matrix multiplications, we consider methods for randomized matrix multiplications and demonstrate that they require less memory with a moderate decrease of the test accuracy. Also, we investigate the variance of the gradient estimate induced by the randomized matrix multiplication. We compare this variance with the variance coming from gradient estimation based on the batch of samples. We demonstrate the benefits of the proposed method on the fine-tuning of the pre-trained RoBERTa model on GLUE tasks.


KSD Aggregated Goodness-of-fit Test.

Antonin Schrab, Benjamin Guedj, Arthur Gretton

Abstract: We investigate properties of goodness-of-fit tests based on the Kernel Stein Discrepancy (KSD). We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. KSDAgg avoids splitting the data to perform kernel selection (which leads to a loss in test power), and rather maximises the test power over a collection of kernels. We provide theoretical guarantees on the power of KSDAgg: we show it achieves the smallest uniform separation rate of the collection, up to a logarithmic term. KSDAgg can be computed exactly in practice as it relies either on a parametric bootstrap or on a wild bootstrap to estimate the quantiles and the level corrections. In particular, for the crucial choice of bandwidth of a fixed kernel, it avoids resorting to arbitrary heuristics (such as median or standard deviation) or to data splitting. We find on both synthetic and real-world data that KSDAgg outperforms other state-of-the-art adaptive KSD-based goodness-of-fit testing procedures.


Algorithms for Efficiently Learning Low-Rank Neural Networks.

Kiran Vodrahalli, Rakesh Shivanna, Maheswaran Sathiamoorthy, Sagar Jain, Ed H. Chi

Abstract: We study algorithms for learning low-rank neural networks -- networks where the weight parameters are re-parameterized by products of two low-rank matrices. First, we present a provably efficient algorithm which learns an optimal low-rank approximation to a single-hidden-layer ReLU network up to additive error $\epsilon$ with probability $\ge 1 - \delta$, given access to noiseless samples with Gaussian marginals in polynomial time and samples. Thus, we provide the first example of an algorithm which can efficiently learn a neural network up to additive error without assuming the ground truth is realizable. To solve this problem, we introduce an efficient SVD-based $\textit{Nonlinear Kernel Projection}$ algorithm for solving a nonlinear low-rank approximation problem over Gaussian space. Inspired by the efficiency of our algorithm, we propose a novel low-rank initialization framework for training low-rank $\textit{deep}$ networks, and prove that for ReLU networks, the gap between our method and existing schemes widens as the desired rank of the approximating weights decreases, or as the dimension of the inputs increases (the latter point holds when network width is superlinear in dimension). Finally, we validate our theory by training ResNet and EfficientNet models on ImageNet.


Improving Screening Processes via Calibrated Subset Selection.

Lequn Wang, Thorsten Joachims, Manuel Gomez Rodriguez

Abstract: Many selection processes such as finding patients qualifying for a medical trial or retrieval pipelines in search engines consist of multiple stages, where an initial screening stage focuses the resources on shortlisting the most promising candidates. In this paper, we investigate what guarantees a screening classifier can provide, independently of whether it is constructed manually or trained. We find that current solutions do not enjoy distribution-free theoretical guarantees -- we show that, in general, even for a perfectly calibrated classifier, there always exist specific pools of candidates for which its shortlist is suboptimal. Then, we develop a distribution-free screening algorithm -- called Calibrated Subset Selection (CSS) -- that, given any classifier and some amount of calibration data, finds near-optimal shortlists of candidates that contain a desired number of qualified candidates in expectation. Moreover, we show that a variant of our algorithm that calibrates a given classifier multiple times across specific groups can create shortlists with provable diversity guarantees. Experiments on US Census survey data validate our theoretical results and show that the shortlists provided by our algorithm are superior to those provided by several competitive baselines.