OpenRaiser/Intern-Atlas huggingface dataset:
Minimal Sample Subspace Learning: Theory and Algorithms
Venue: Journal JMLR 2019
Year: 2019

Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and conditional uniqueness of MSS are discussed with conditions generally satisfied in applications. Utilizing weak prior information of MSS, the minimality inspection of segments is further simplified to the prior detection of partitions. The MSS problem is then modeled as a computable optimization problem via self-expressiveness of samples. A closed form of representation matrices is first given for the self-expressiveness, and the connection of diagonal blocks is then addressed. The MSS model uses a rank restriction on the sum of segment ranks. Theoretically, it can retrieve the minimal sample subspaces that could be heavily intersected. The optimization problem is solved via a basic manifold conjugate gradient algorithm, alternative optimization and hybrid optimization, taking into account of solving both the primal MSS problem and its pseudo-dual problem. The MSS model is further modified for handling noisy data, and solved by an ADMM algorithm. The reported experiments show the strong ability of the MSS method on retrieving minimal sample subspaces that are heavily intersected.
Stochastic Canonical Correlation Analysis
Venue: Journal JMLR 2019
Year: 2019

We study the sample complexity of canonical correlation analysis (CCA), \ie, the number of samples needed to estimate the population canonical correlation and directions up to arbitrarily small error. With mild assumptions on the data distribution, we show that in order to achieve $ε$-suboptimality in a properly defined measure of alignment between the estimated canonical directions and the population solution, we can solve the empirical objective exactly with $N(ε, Δ, γ)$ samples, where $Δ$ is the singular value gap of the whitened cross-covariance matrix and $1/γ$ is an upper bound of the condition number of auto-covariance matrices. Moreover, we can achieve the same learning accuracy by drawing the same level of samples and solving the empirical objective approximately with a stochastic optimization algorithm; this algorithm is based on the shift-and-invert power iterations and only needs to process the dataset for $\mathcal{O}\left(\log \frac{1}ε \right)$ passes. Finally, we show that, given an estimate of the canonical correlation, the streaming version of the shift-and-invert power iterations achieves the same learning accuracy with the same level of sample complexity, by processing the data only once.
Monotone Learning with Rectified Wire Networks
Venue: Journal JMLR 2019
Year: 2019

We introduce a new neural network model, together with a tractable and monotone online learning algorithm. Our model describes feed-forward networks for classification, with one output node for each class. The only nonlinear operation is rectification using a ReLU function with a bias. However, there is a rectifier on every edge rather than at the nodes of the network. There are also weights, but these are positive, static, and associated with the nodes. Our "rectified wire" networks are able to represent arbitrary Boolean functions. Only the bias parameters, on the edges of the network, are learned. Another departure in our approach, from standard neural networks, is that the loss function is replaced by a constraint. This constraint is simply that the value of the output node associated with the correct class should be zero. Our model has the property that the exact norm-minimizing parameter update, required to correctly classify a training item, is the solution to a quadratic program that can be computed with a few passes through the network. We demonstrate a training algorithm using this update, called sequential deactivation (SDA), on MNIST and some synthetic datasets. Upon adopting a natural choice for the nodal weights, SDA has no hyperparameters other than those describing the network structure. Our experiments explore behavior with respect to network size and depth in a family of sparse expander networks.
Unsupervised Basis Function Adaptation for Reinforcement Learning
Venue: Journal JMLR 2019
Year: 2019

When using reinforcement learning (RL) algorithms it is common, given a large state space, to introduce some form of approximation architecture for the value function (VF). The exact form of this architecture can have a significant effect on an agent's performance, however, and determining a suitable approximation architecture can often be a highly complex task. Consequently there is currently interest among researchers in the potential for allowing RL algorithms to adaptively generate (i.e. to learn) approximation architectures. One relatively unexplored method of adapting approximation architectures involves using feedback regarding the frequency with which an agent has visited certain states to guide which areas of the state space to approximate with greater detail. In this article we will: (a) informally discuss the potential advantages offered by such methods; (b) introduce a new algorithm based on such methods which adapts a state aggregation approximation architecture on-line and is designed for use in conjunction with SARSA; (c) provide theoretical results, in a policy evaluation setting, regarding this particular algorithm's complexity, convergence properties and potential to reduce VF error; and finally (d) test experimentally the extent to which this algorithm can improve performance given a number of different test problems. Taken together our results suggest that our algorithm (and potentially such methods more generally) can provide a versatile and computationally lightweight means of significantly boosting RL performance given suitable conditions which are commonly encountered in practice.
Deep Reinforcement Learning for Swarm Systems
Venue: Journal JMLR 2019
Year: 2019

Recently, deep reinforcement learning (RL) methods have been applied successfully to multi-agent scenarios. Typically, these methods rely on a concatenation of agent states to represent the information content required for decentralized decision making. However, concatenation scales poorly to swarm systems with a large number of homogeneous agents as it does not exploit the fundamental properties inherent to these systems: (i) the agents in the swarm are interchangeable and (ii) the exact number of agents in the swarm is irrelevant. Therefore, we propose a new state representation for deep multi-agent RL based on mean embeddings of distributions. We treat the agents as samples of a distribution and use the empirical mean embedding as input for a decentralized policy. We define different feature spaces of the mean embedding using histograms, radial basis functions and a neural network learned end-to-end. We evaluate the representation on two well known problems from the swarm literature (rendezvous and pursuit evasion), in a globally and locally observable setup. For the local setup we furthermore introduce simple communication protocols. Of all approaches, the mean embedding representation using neural network features enables the richest information exchange between neighboring agents facilitating the development of more complex collective strategies.
Measuring the Effects of Data Parallelism on Neural Network Training
Venue: Journal JMLR 2019
Year: 2019

Recent hardware developments have dramatically increased the scale of data parallelism available for neural network training. Among the simplest ways to harness next-generation hardware is to increase the batch size in standard mini-batch neural network training algorithms. In this work, we aim to experimentally characterize the effects of increasing the batch size on training time, as measured by the number of steps necessary to reach a goal out-of-sample error. We study how this relationship varies with the training algorithm, model, and data set, and find extremely large variation between workloads. Along the way, we show that disagreements in the literature on how batch size affects model quality can largely be explained by differences in metaparameter tuning and compute budgets at different batch sizes. We find no evidence that larger batch sizes degrade out-of-sample performance. Finally, we discuss the implications of our results on efforts to train neural networks much faster in the future. Our experimental data is publicly available as a database of 71,638,836 loss measurements taken over the course of training for 168,160 individual models across 35 workloads.
PyOD: A Python Toolbox for Scalable Outlier Detection
Venue: Journal JMLR 2019
Year: 2019

PyOD is an open-source Python toolbox for performing scalable outlier detection on multivariate data. Uniquely, it provides access to a wide range of outlier detection algorithms, including established outlier ensembles and more recent neural network-based approaches, under a single, well-documented API designed for use by both practitioners and researchers. With robustness and scalability in mind, best practices such as unit testing, continuous integration, code coverage, maintainability checks, interactive examples and parallelization are emphasized as core components in the toolbox's development. PyOD is compatible with both Python 2 and 3 and can be installed through Python Package Index (PyPI) or https://github.com/yzhao062/pyod.
Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery
Venue: Journal JMLR 2019
Year: 2019

Nonconvex matrix recovery is known to contain no spurious local minima under a restricted isometry property (RIP) with a sufficiently small RIP constant $δ$. If $δ$ is too large, however, then counterexamples containing spurious local minima are known to exist. In this paper, we introduce a proof technique that is capable of establishing sharp thresholds on $δ$ to guarantee the inexistence of spurious local minima. Using the technique, we prove that in the case of a rank-1 ground truth, an RIP constant of $δ<1/2$ is both necessary and sufficient for exact recovery from any arbitrary initial point (such as a random point). We also prove a local recovery result: given an initial point $x_{0}$ satisfying $f(x_{0})\le(1-δ)^{2}f(0)$, any descent algorithm that converges to second-order optimality guarantees exact recovery.
Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learning
Venue: Journal JMLR 2019
Year: 2019

Revealing latent structure in data is an active field of research, having introduced exciting technologies such as variational autoencoders and adversarial networks, and is essential to push machine learning towards unsupervised knowledge discovery. However, a major challenge is the lack of suitable benchmarks for an objective and quantitative evaluation of learned representations. To address this issue we introduce Morpho-MNIST, a framework that aims to answer: "to what extent has my model learned to represent specific factors of variation in the data?" We extend the popular MNIST dataset by adding a morphometric analysis enabling quantitative comparison of trained models, identification of the roles of latent variables, and characterisation of sample diversity. We further propose a set of quantifiable perturbations to assess the performance of unsupervised and supervised methods on challenging tasks such as outlier detection and domain adaptation. Data and code are available at https://github.com/dccastro/Morpho-MNIST.
SimpleDet: A Simple and Versatile Distributed Framework for Object Detection and Instance Recognition
Venue: Journal JMLR 2019
Year: 2019

Object detection and instance recognition play a central role in many AI applications like autonomous driving, video surveillance and medical image analysis. However, training object detection models on large scale datasets remains computationally expensive and time consuming. This paper presents an efficient and open source object detection framework called SimpleDet which enables the training of state-of-the-art detection models on consumer grade hardware at large scale. SimpleDet supports up-to-date detection models with best practice. SimpleDet also supports distributed training with near linear scaling out of box. Codes, examples and documents of SimpleDet can be found at https://github.com/tusimple/simpledet .
Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming
Venue: Journal JMLR 2019
Year: 2019

We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong to known random subspaces of dimensions $k$ and $n$, then they can be recovered up to the inherent scaling ambiguity with $m \gg (k+n) \log^2 m$ phaseless measurements. Our method provides the first theoretical recovery guarantee for this problem by a computationally efficient algorithm and does not require a solution estimate to be computed for initialization. Our proof is based on Rademacher complexity estimates. Additionally, we provide an alternating direction method of multipliers (ADMM) implementation and provide numerical experiments that verify the theory.
GraSPy: Graph Statistics in Python
Venue: Journal JMLR 2019
Year: 2019

We introduce GraSPy, a Python library devoted to statistical inference, machine learning, and visualization of random graphs and graph populations. This package provides flexible and easy-to-use algorithms for analyzing and understanding graphs with a scikit-learn compliant API. GraSPy can be downloaded from Python Package Index (PyPi), and is released under the Apache 2.0 open-source license. The documentation and all releases are available at https://neurodata.io/graspy.
Why do deep convolutional networks generalize so poorly to small image transformations?
Venue: Journal JMLR 2019
Year: 2019

Convolutional Neural Networks (CNNs) are commonly assumed to be invariant to small image transformations: either because of the convolutional architecture or because they were trained using data augmentation. Recently, several authors have shown that this is not the case: small translations or rescalings of the input image can drastically change the network's prediction. In this paper, we quantify this phenomena and ask why neither the convolutional architecture nor data augmentation are sufficient to achieve the desired invariance. Specifically, we show that the convolutional architecture does not give invariance since architectures ignore the classical sampling theorem, and data augmentation does not give invariance because the CNNs learn to be invariant to transformations only for images that are very similar to typical images from the training set. We discuss two possible solutions to this problem: (1) antialiasing the intermediate representations and (2) increasing data augmentation and show that they provide only a partial solution at best. Taken together, our results indicate that the problem of insuring invariance to small image transformations in neural networks while preserving high accuracy remains unsolved.
Joint Causal Inference from Multiple Contexts
Venue: Journal JMLR 2020
Year: 2020

The gold standard for discovering causal relations is by means of experimentation. Over the last decades, alternative methods have been proposed that can infer causal relations between variables from certain statistical patterns in purely observational data. We introduce Joint Causal Inference (JCI), a novel approach to causal discovery from multiple data sets from different contexts that elegantly unifies both approaches. JCI is a causal modeling framework rather than a specific algorithm, and it can be implemented using any causal discovery algorithm that can take into account certain background knowledge. JCI can deal with different types of interventions (e.g., perfect, imperfect, stochastic, etc.) in a unified fashion, and does not require knowledge of intervention targets or types in case of interventional data. We explain how several well-known causal discovery algorithms can be seen as addressing special cases of the JCI framework, and we also propose novel implementations that extend existing causal discovery methods for purely observational data to the JCI setting. We evaluate different JCI implementations on synthetic data and on flow cytometry protein expression data and conclude that JCI implementations can considerably outperform state-of-the-art causal discovery algorithms.
New Insights and Perspectives on the Natural Gradient Method
Venue: Journal JMLR 2020
Year: 2020

Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically analyze this method and its properties, and show how it can be viewed as a type of 2nd-order optimization method, with the Fisher information matrix acting as a substitute for the Hessian. In many important cases, the Fisher information matrix is shown to be equivalent to the Generalized Gauss-Newton matrix, which both approximates the Hessian, but also has certain properties that favor its use over the Hessian. This perspective turns out to have significant implications for the design of a practical and robust natural gradient optimizer, as it motivates the use of techniques like trust regions and Tikhonov regularization. Additionally, we make a series of contributions to the understanding of natural gradient and 2nd-order methods, including: a thorough analysis of the convergence speed of stochastic natural gradient descent (and more general stochastic 2nd-order methods) as applied to convex quadratics, a critical examination of the oft-used "empirical" approximation of the Fisher matrix, and an analysis of the (approximate) parameterization invariance property possessed by natural gradient methods (which we show also holds for certain other curvature, but notably not the Hessian).
Tensor Train Decomposition on TensorFlow (T3F)
Venue: Journal JMLR 2020
Year: 2020

Tensor Train decomposition is used across many branches of machine learning. We present T3F -- a library for Tensor Train decomposition based on TensorFlow. T3F supports GPU execution, batch processing, automatic differentiation, and versatile functionality for the Riemannian optimization framework, which takes into account the underlying manifold structure to construct efficient optimization methods. The library makes it easier to implement machine learning papers that rely on the Tensor Train decomposition. T3F includes documentation, examples and 94% test coverage.
Stochastic Nested Variance Reduction for Nonconvex Optimization
Venue: Journal JMLR 2020
Year: 2020

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference points to construct a semi-stochastic gradient with diminishing variance in each iteration, our algorithm uses $K+1$ nested reference points to build a semi-stochastic gradient to further reduce its variance in each iteration. For smooth nonconvex functions, the proposed algorithm converges to an $ε$-approximate first-order stationary point (i.e., $\|\nabla F(\mathbf{x})\|_2\leq ε$) within $\tilde O(n\land ε^{-2}+ε^{-3}\land n^{1/2}ε^{-2})$ number of stochastic gradient evaluations. This improves the best known gradient complexity of SVRG $O(n+n^{2/3}ε^{-2})$ and that of SCSG $O(n\land ε^{-2}+ε^{-10/3}\land n^{2/3}ε^{-2})$. For gradient dominated functions, our algorithm also achieves better gradient complexity than the state-of-the-art algorithms. Thorough experimental results on different nonconvex optimization problems back up our theory.
Learning Sums of Independent Random Variables with Sparse Collective Support
Venue: Journal JMLR 2020
Year: 2020

We study the learnability of sums of independent integer random variables given a bound on the size of the union of their supports. For $\mathcal{A} \subset \mathbf{Z}_{+}$, a sum of independent random variables with collective support $\mathcal{A}$} (called an $\mathcal{A}$-sum in this paper) is a distribution $\mathbf{S} = \mathbf{X}_1 + \cdots + \mathbf{X}_N$ where the $\mathbf{X}_i$'s are mutually independent (but not necessarily identically distributed) integer random variables with $\cup_i \mathsf{supp}(\mathbf{X}_i) \subseteq \mathcal{A}.$ We give two main algorithmic results for learning such distributions: 1. For the case $| \mathcal{A} | = 3$, we give an algorithm for learning $\mathcal{A}$-sums to accuracy $ε$ that uses $\mathsf{poly}(1/ε)$ samples and runs in time $\mathsf{poly}(1/ε)$, independent of $N$ and of the elements of $\mathcal{A}$. 2. For an arbitrary constant $k \geq 4$, if $\mathcal{A} = \{ a_1,...,a_k\}$ with $0 \leq a_1 < ... < a_k$, we give an algorithm that uses $\mathsf{poly}(1/ε) \cdot \log \log a_k$ samples (independent of $N$) and runs in time $\mathsf{poly}(1/ε, \log a_k).$ We prove an essentially matching lower bound: if $|\mathcal{A}| = 4$, then any algorithm must use $Ω(\log \log a_4) $ samples even for learning to constant accuracy. We also give similar-in-spirit (but quantitatively very different) algorithmic results, and essentially matching lower bounds, for the case in which $\mathcal{A}$ is not known to the learner.
Learning and Interpreting Multi-Multi-Instance Learning Networks
Venue: Journal JMLR 2020
Year: 2020

We introduce an extension of the multi-instance learning problem where examples are organized as nested bags of instances (e.g., a document could be represented as a bag of sentences, which in turn are bags of words). This framework can be useful in various scenarios, such as text and image classification, but also supervised learning over graphs. As a further advantage, multi-multi instance learning enables a particular way of interpreting predictions and the decision function. Our approach is based on a special neural network layer, called bag-layer, whose units aggregate bags of inputs of arbitrary size. We prove theoretically that the associated class of functions contains all Boolean functions over sets of sets of instances and we provide empirical evidence that functions of this kind can be actually learned on semi-synthetic datasets. We finally present experiments on text classification, on citation graphs, and social graph data, which show that our model obtains competitive results with respect to accuracy when compared to other approaches such as convolutional networks on graphs, while at the same time it supports a general approach to interpret the learnt model, as well as explain individual predictions.