pwc-archive/papers-with-abstracts huggingface dataset:
Enhancing Generative Models via Quantum Correlations
Authors: Xun Gao, Eric R. Anschuetz, Sheng-Tao Wang, J. Ignacio Cirac, Mikhail D. Lukin
Date: 2021-01-20 00:00:00
Tasks: BIG-bench Machine Learning, Quantum Machine Learning

Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely-used generative models, known as Bayesian networks, and its minimal quantum extension. We show that this expressivity advantage is associated with quantum nonlocality and quantum contextuality. Furthermore, we numerically test this separation on standard machine learning data sets and show that it holds for practical problems. The possibility of quantum advantage demonstrated in this work not only sheds light on the design of useful quantum machine learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.
Optimal Full Ranking from Pairwise Comparisons
Authors: Pinhan Chen, Chao GAO, Anderson Y. Zhang
Date: 2021-01-21 00:00:00

We consider the problem of ranking $n$ players from partial pairwise comparison data under the Bradley-Terry-Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendall's tau distance that measures the difference between two rank vectors by counting the number of inversions. The minimax rate of ranking exhibits a transition between an exponential rate and a polynomial rate depending on the magnitude of the signal-to-noise ratio of the problem. To the best of our knowledge, this phenomenon is unique to full ranking and has not been seen in any other statistical estimation problem. To achieve the minimax rate, we propose a divide-and-conquer ranking algorithm that first divides the $n$ players into groups of similar skills and then computes local MLE within each group. The optimality of the proposed algorithm is established by a careful approximate independence argument between the two steps.
Robust Reinforcement Learning on State Observations with Learned Optimal Adversary
Authors: huan zhang, Hongge Chen, Duane Boning, Cho-Jui Hsieh
Date: 2021-01-21 00:00:00
Proceeding: ICLR 2021 1
Tasks: Adversarial Attack, continuous-control, Continuous Control, Deep Reinforcement Learning, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

We study the robustness of reinforcement learning (RL) with adversarially perturbed state observations, which aligns with the setting of many adversarial attacks to deep reinforcement learning (DRL) and is also important for rolling out real-world RL agent under unpredictable sensing noise. With a fixed agent policy, we demonstrate that an optimal adversary to perturb state observations can be found, which is guaranteed to obtain the worst case agent reward. For DRL settings, this leads to a novel empirical adversarial attack to RL agents via a learned adversary that is much stronger than previous ones. To enhance the robustness of an agent, we propose a framework of alternating training with learned adversaries (ATLA), which trains an adversary online together with the agent using policy gradient following the optimal adversarial attack framework. Additionally, inspired by the analysis of state-adversarial Markov decision process (SA-MDP), we show that past states and actions (history) can be useful for learning a robust agent, and we empirically find a LSTM based policy can be more robust under adversaries. Empirical evaluations on a few continuous control environments show that ATLA achieves state-of-the-art performance under strong adversaries. Our code is available at https://github.com/huanzhang12/ATLA_robust_RL.
Estimating Average Treatment Effects via Orthogonal Regularization
Authors: Tobias Hatt, Stefan Feuerriegel
Date: 2021-01-21 00:00:00
Tasks: Decision Making

Decision-making often requires accurate estimation of treatment effects from observational data. This is challenging as outcomes of alternative decisions are not observed and have to be estimated. Previous methods estimate outcomes based on unconfoundedness but neglect any constraints that unconfoundedness imposes on the outcomes. In this paper, we propose a novel regularization framework for estimating average treatment effects that exploits unconfoundedness. To this end, we formalize unconfoundedness as an orthogonality constraint, which ensures that the outcomes are orthogonal to the treatment assignment. This orthogonality constraint is then included in the loss function via a regularization. Based on our regularization framework, we develop deep orthogonal networks for unconfounded treatments (DONUT), which learn outcomes that are orthogonal to the treatment assignment. Using a variety of benchmark datasets for estimating average treatment effects, we demonstrate that DONUT outperforms the state-of-the-art substantially.
Out-of-Distribution Generalization Analysis via Influence Function
Authors: Haotian Ye, Chuanlong Xie, Yue Liu, Zhenguo Li
Date: 2021-01-21 00:00:00
Tasks: Out-of-Distribution Generalization

The mismatch between training and target data is one major challenge for current machine learning systems. When training data is collected from multiple domains and the target domains include all training domains and other new domains, we are facing an Out-of-Distribution (OOD) generalization problem that aims to find a model with the best OOD accuracy. One of the definitions of OOD accuracy is worst-domain accuracy. In general, the set of target domains is unknown, and the worst over target domains may be unseen when the number of observed domains is limited. In this paper, we show that the worst accuracy over the observed domains may dramatically fail to identify the OOD accuracy. To this end, we introduce Influence Function, a classical tool from robust statistics, into the OOD generalization problem and suggest the variance of influence function to monitor the stability of a model on training domains. We show that the accuracy on test domains and the proposed index together can help us discern whether OOD algorithms are needed and whether a model achieves good OOD generalization.
Orthogonal Least Squares Based Fast Feature Selection for Linear Classification
Authors: Sikai Zhang, Zi-Qiang Lang
Date: 2021-01-21 00:00:00
Tasks: Classification, feature selection, General Classification

An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in OLS and used as the feature ranking criterion. The equivalence between the canonical correlation coefficient, Fisher's criterion, and the sum of the SOCCs is revealed, which unveils the statistical implication of ERR in OLS for the first time. It is also shown that the OLS based feature selection method has speed advantages when applied for greedy search. The proposed method is comprehensively compared with the mutual information based feature selection methods and the embedded methods using both synthetic and real world datasets. The results show that the proposed method is always in the top 5 among the 12 candidate methods. Besides, the proposed method can be directly applied to continuous features without discretisation, which is another significant advantage over mutual information based methods.
Dive into Decision Trees and Forests: A Theoretical Demonstration
Authors: Jinxiong Zhang
Date: 2021-01-20 00:00:00
Tasks: Information Retrieval, Recommendation Systems, Retrieval

Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and labels into smaller ones. While decision trees have a long history, recent advances have greatly improved their performance in computational advertising, recommender system, information retrieval, etc. We introduce common tree-based models (e.g., Bayesian CART, Bayesian regression splines) and training techniques (e.g., mixed integer programming, alternating optimization, gradient descent). Along the way, we highlight probabilistic characteristics of tree-based models and explain their practical and theoretical benefits. Except machine learning and data mining, we try to show theoretical advances on tree-based models from other fields such as statistics and operation research. We list the reproducible resource at the end of each method.
A New Knowledge Gradient-based Method for Constrained Bayesian Optimization
Authors: Wenjie Chen, Shengcai Liu, Ke Tang
Date: 2021-01-20 00:00:00
Tasks: Bayesian Optimization

Black-box problems are common in real life like structural design, drug experiments, and machine learning. When optimizing black-box systems, decision-makers always consider multiple performances and give the final decision by comprehensive evaluations. Motivated by such practical needs, we focus on constrained black-box problems where the objective and constraints lack known special structure, and evaluations are expensive and even with noise. We develop a novel constrained Bayesian optimization approach based on the knowledge gradient method ($c-\rm{KG}$). A new acquisition function is proposed to determine the next batch of samples considering optimality and feasibility. An unbiased estimator of the gradient of the new acquisition function is derived to implement the $c-\rm{KG}$ approach.
Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem
Authors: Matthew J. Colbrook, Vegard Antun, Anders C. Hansen
Date: 2021-01-20 00:00:00

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence of stable neural networks (NNs). We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities, however, there does not exist any algorithm, even randomised, that can train (or compute) such a NN. For any positive integers $K > 2$ and $L$, there are cases where simultaneously: (a) no randomised training algorithm can compute a NN correct to $K$ digits with probability greater than $1/2$, (b) there exists a deterministic training algorithm that computes a NN with $K-1$ correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic training algorithm that computes a NN with $K-2$ correct digits using no more than $L$ training samples. These results imply a classification theory describing conditions under which (stable) NNs with a given accuracy can be computed by an algorithm. We begin this theory by establishing sufficient conditions for the existence of algorithms that compute stable NNs in inverse problems. We introduce Fast Iterative REstarted NETworks (FIRENETs), which we both prove and numerically verify are stable. Moreover, we prove that only $\mathcal{O}(|\log(\epsilon)|)$ layers are needed for an $\epsilon$-accurate solution to the inverse problem.
Non-Convex Compressed Sensing with Training Data
Authors: G. Welper
Date: 2021-01-20 00:00:00
Tasks: compressed sensing

Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and without any assumptions on $A$ the problem is $NP$-hard. A common approach is to replace $\ell_1$ by $\ell_p$ minimization for $0 < p < 1$, which is no longer convex and typically requires some form of local initial values for provably convergent algorithms. In this paper, we consider an alternative, where instead of suitable initial values we are provided with extra training problems $Ax = B_l$, $l=1, \dots, p$ that are related to our compressed sensing problem. They allow us to find the solution of the original problem $Ax = b$ with high probability in the range of a one layer linear neural network with comparatively few assumptions on the matrix $A$.
Ensemble manifold based regularized multi-modal graph convolutional network for cognitive ability prediction
Authors: Gang Qu, Li Xiao, Wenxing Hu, Kun Zhang, Vince D. Calhoun, Yu-Ping Wang
Date: 2021-01-20 00:00:00
Tasks: Functional Connectivity, Graph Embedding, Time Series Analysis

Objective: Multi-modal functional magnetic resonance imaging (fMRI) can be used to make predictions about individual behavioral and cognitive traits based on brain connectivity networks. Methods: To take advantage of complementary information from multi-modal fMRI, we propose an interpretable multi-modal graph convolutional network (MGCN) model, incorporating the fMRI time series and the functional connectivity (FC) between each pair of brain regions. Specifically, our model learns a graph embedding from individual brain networks derived from multi-modal data. A manifold-based regularization term is then enforced to consider the relationships of subjects both within and between modalities. Furthermore, we propose the gradient-weighted regression activation mapping (Grad-RAM) and the edge mask learning to interpret the model, which is used to identify significant cognition-related biomarkers. Results: We validate our MGCN model on the Philadelphia Neurodevelopmental Cohort to predict individual wide range achievement test (WRAT) score. Our model obtains superior predictive performance over GCN with a single modality and other competing approaches. The identified biomarkers are cross-validated from different approaches. Conclusion and Significance: This paper develops a new interpretable graph deep learning framework for cognitive ability prediction, with the potential to overcome the limitations of several current data-fusion models. The results demonstrate the power of MGCN in analyzing multi-modal fMRI and discovering significant biomarkers for human brain studies.
Marius: Learning Massive Graph Embeddings on a Single Machine
Authors: Jason Mohoney, Roger Waleffe, Yiheng Xu, Theodoros Rekatsinas, Shivaram Venkataraman
Date: 2021-01-20 00:00:00
Tasks: CPU, GPU, Graph Embedding

We propose a new framework for computing the embeddings of large-scale graphs on a single machine. A graph embedding is a fixed length vector representation for each node (and/or edge-type) in a graph and has emerged as the de-facto approach to apply modern machine learning on graphs. We identify that current systems for learning the embeddings of large-scale graphs are bottlenecked by data movement, which results in poor resource utilization and inefficient training. These limitations require state-of-the-art systems to distribute training across multiple machines. We propose Marius, a system for efficient training of graph embeddings that leverages partition caching and buffer-aware data orderings to minimize disk access and interleaves data movement with computation to maximize utilization. We compare Marius against two state-of-the-art industrial systems on a diverse array of benchmarks. We demonstrate that Marius achieves the same level of accuracy but is up to one order of magnitude faster. We also show that Marius can scale training to datasets an order of magnitude beyond a single machine's GPU and CPU memory capacity, enabling training of configurations with more than a billion edges and 550 GB of total parameters on a single machine with 16 GB of GPU memory and 64 GB of CPU memory. Marius is open-sourced at www.marius-project.org.
Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs
Authors: Jie Bu, Anuj Karpatne
Date: 2021-01-20 00:00:00
Tasks: Efficient Neural Network

We propose quadratic residual networks (QRes) as a new type of parameter-efficient neural network architecture, by adding a quadratic residual term to the weighted sum of inputs before applying activation functions. With sufficiently high functional capacity (or expressive power), we show that it is especially powerful for solving forward and inverse physics problems involving partial differential equations (PDEs). Using tools from algebraic geometry, we theoretically demonstrate that, in contrast to plain neural networks, QRes shows better parameter efficiency in terms of network width and depth thanks to higher non-linearity in every neuron. Finally, we empirically show that QRes shows faster convergence speed in terms of number of training epochs especially in learning complex patterns.
Better Short than Greedy: Interpretable Models through Optimal Rule Boosting
Authors: Mario Boley, Simon Teshuva, Pierre Le Bodic, Geoffrey I Webb
Date: 2021-01-21 00:00:00

Rule ensembles are designed to provide a useful trade-off between predictive accuracy and model interpretability. However, the myopic and random search components of current rule ensemble methods can compromise this goal: they often need more rules than necessary to reach a certain accuracy level or can even outright fail to accurately model a distribution that can actually be described well with a few rules. Here, we present a novel approach aiming to fit rule ensembles of maximal predictive power for a given ensemble size (and thus model comprehensibility). In particular, we present an efficient branch-and-bound algorithm that optimally solves the per-rule objective function of the popular second-order gradient boosting framework. Our main insight is that the boosting objective can be tightly bounded in linear time of the number of covered data points. Along with an additional novel pruning technique related to rule redundancy, this leads to a computationally feasible approach for boosting optimal rules that, as we demonstrate on a wide range of common benchmark problems, consistently outperforms the predictive performance of boosting greedy rules.
Invariance, encodings, and generalization: learning identity effects with neural networks
Authors: S. Brugiapaglia, M. Liu, P. Tupper
Date: 2021-01-21 00:00:00

Often in language and other areas of cognition, whether two components of an object are identical or not determines if it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from examples, it is easy enough to build in an identify effect. But can identity effects be learned from the data without explicit guidance? We provide a framework in which we can rigorously prove that algorithms satisfying simple criteria cannot make the correct inference. We then show that a broad class of learning algorithms including deep feedforward neural networks trained via gradient-based algorithms (such as stochastic gradient descent or the Adam method) satisfy our criteria, dependent on the encoding of inputs. In some broader circumstances we are able to provide adversarial examples that the network necessarily classifies incorrectly. Finally, we demonstrate our theory with computational experiments in which we explore the effect of different input encodings on the ability of algorithms to generalize to novel inputs. This allows us to show similar effects to those predicted by theory for more realistic methods that violate some of the conditions of our theoretical results.
A Survey on Ensemble Learning under the Era of Deep Learning
Authors: Yongquan Yang, Haijun Lv, Ning Chen
Date: 2021-01-21 00:00:00
Tasks: Deep Learning, Ensemble Learning

Due to the dominant position of deep learning (mostly deep neural networks) in various artificial intelligence applications, recently, ensemble learning based on deep neural networks (ensemble deep learning) has shown significant performances in improving the generalization of learning system. However, since modern deep neural networks usually have millions to billions of parameters, the time and space overheads for training multiple base deep learners and testing with the ensemble deep learner are far greater than that of traditional ensemble learning. Though several algorithms of fast ensemble deep learning have been proposed to promote the deployment of ensemble deep learning in some applications, further advances still need to be made for many applications in specific fields, where the developing time and computing resources are usually restricted or the data to be processed is of large dimensionality. An urgent problem needs to be solved is how to take the significant advantages of ensemble deep learning while reduce the required expenses so that many more applications in specific fields can benefit from it. For the alleviation of this problem, it is essential to know about how ensemble learning has developed under the era of deep learning. Thus, in this article, we present fundamental discussions focusing on data analyses of published works, methodologies, recent advances and unattainability of traditional ensemble learning and ensemble deep learning. We hope this article will be helpful to realize the intrinsic problems and technical challenges faced by future developments of ensemble learning under the era of deep learning.
An Information-Theoretic Analysis of the Impact of Task Similarity on Meta-Learning
Authors: Sharu Theresa Jose, Osvaldo Simeone
Date: 2021-01-21 00:00:00
Tasks: Meta-Learning

Meta-learning aims at optimizing the hyperparameters of a model class or training algorithm from the observation of data from a number of related tasks. Following the setting of Baxter [1], the tasks are assumed to belong to the same task environment, which is defined by a distribution over the space of tasks and by per-task data distributions. The statistical properties of the task environment thus dictate the similarity of the tasks. The goal of the meta-learner is to ensure that the hyperparameters obtain a small loss when applied for training of a new task sampled from the task environment. The difference between the resulting average loss, known as meta-population loss, and the corresponding empirical loss measured on the available data from related tasks, known as meta-generalization gap, is a measure of the generalization capability of the meta-learner. In this paper, we present novel information-theoretic bounds on the average absolute value of the meta-generalization gap. Unlike prior work [2], our bounds explicitly capture the impact of task relatedness, the number of tasks, and the number of data samples per task on the meta-generalization gap. Task similarity is gauged via the Kullback-Leibler (KL) and Jensen-Shannon (JS) divergences. We illustrate the proposed bounds on the example of ridge regression with meta-learned bias.
Analysis of Information Flow Through U-Nets
Authors: Suemin Lee, Ivan V. Bajić
Date: 2021-01-21 00:00:00
Tasks: Image Segmentation, Semantic Segmentation

Deep Neural Networks (DNNs) have become ubiquitous in medical image processing and analysis. Among them, U-Nets are very popular in various image segmentation tasks. Yet, little is known about how information flows through these networks and whether they are indeed properly designed for the tasks they are being proposed for. In this paper, we employ information-theoretic tools in order to gain insight into information flow through U-Nets. In particular, we show how mutual information between input/output and an intermediate layer can be a useful tool to understand information flow through various portions of a U-Net, assess its architectural efficiency, and even propose more efficient designs.