pwc-archive/papers-with-abstracts huggingface dataset:
A theory of representation learning gives a deep generalisation of kernel methods
Authors: Adam X. Yang, Maxime Robeyns, Edward Milsom, Ben Anson, Nandi Schoots, Laurence Aitchison
Date: 2021-08-30 00:00:00
Tasks: Bayesian Inference, Gaussian Processes, Representation Learning

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.
Multimodal Data Fusion in High-Dimensional Heterogeneous Datasets via Generative Models
Authors: Yasin Yilmaz, Mehmet Aktukmak, Alfred O. Hero
Date: 2021-08-27 00:00:00
Tasks: Anomaly Detection, Imputation, Recommendation Systems, Vocal Bursts Intensity Prediction

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do not readily extend to heterogeneous data that are a combination of numerical and categorical variables, e.g., arising from linked GPS and text data. In this paper, we are interested in learning probabilistic generative models from high-dimensional heterogeneous data in an unsupervised fashion. The learned generative model provides latent unified representations that capture the factors common to the multiple dimensions of the data, and thus enable fusing multimodal data for various machine learning tasks. Following a Bayesian approach, we propose a general framework that combines disparate data types through the natural parameterization of the exponential family of distributions. To scale the model inference to millions of instances with thousands of features, we use the Laplace-Bernstein approximation for posterior computations involving nonlinear link functions. The proposed algorithm is presented in detail for the commonly encountered heterogeneous datasets with real-valued (Gaussian) and categorical (multinomial) features. Experiments on two high-dimensional and heterogeneous datasets (NYC Taxi and MovieLens-10M) demonstrate the scalability and competitive performance of the proposed algorithm on different machine learning tasks such as anomaly detection, data imputation, and recommender systems.
Approximate Bayesian Optimisation for Neural Networks
Authors: Nadhir Hassen, Irina Rish
Date: 2021-08-27 00:00:00
Tasks: Bayesian Optimisation, Density Ratio Estimation, Gaussian Processes

A body of work has been done to automate machine learning algorithm to highlight the importance of model choice. Automating the process of choosing the best forecasting model and its corresponding parameters can result to improve a wide range of real-world applications. Bayesian optimisation (BO) uses a blackbox optimisation methods to propose solutions according to an exploration-exploitation trade-off criterion through acquisition functions. BO framework imposes two key ingredients: a probabilistic surrogate model that consist of prior belief of the unknown objective function(data-dependant) and an objective function that describes how optimal is the model-fit. Choosing the best model and its associated hyperparameters can be very expensive, and is typically fit using Gaussian processes (GPs) and at some extends applying approximate inference due its intractability. However, since GPs scale cubically with the number of observations, it has been challenging to handle objectives whose optimization requires many evaluations. In addition, most real-dataset are non-stationary which make idealistic assumptions on surrogate models. The necessity to solve the analytical tractability and the computational feasibility in a stochastic fashion enables to ensure the efficiency and the applicability of Bayesian optimisation. In this paper we explore the use of neural networks as an alternative to GPs to model distributions over functions, we provide a link between density-ratio estimation and class probability estimation based on approximate inference, this reformulation provides algorithm efficiency and tractability.
Convergence Rates for Learning Linear Operators from Noisy Data
Authors: Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen, Andrew M. Stuart
Date: 2021-08-27 00:00:00
Tasks: Learning Theory

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assuming that the operator is diagonalizable in a known basis, this work solves the equivalent inverse problem of estimating the operator's eigenvalues given the data. Adopting a Bayesian approach, the theoretical analysis establishes posterior contraction rates in the infinite data limit with Gaussian priors that are not directly linked to the forward map of the inverse problem. The main results also include learning-theoretic generalization error guarantees for a wide range of distribution shifts. These convergence rates quantify the effects of data smoothness and true eigenvalue decay or growth, for compact or unbounded operators, respectively, on sample complexity. Numerical evidence supports the theory in diagonal and non-diagonal settings.
Dynamic Selection in Algorithmic Decision-making
Authors: Jin Li, Ye Luo, Xiaowei Zhang
Date: 2021-08-28 00:00:00
Tasks: Decision Making

This paper identifies and addresses dynamic selection problems in online learning algorithms with endogenous data. In a contextual multi-armed bandit model, a novel bias (self-fulfilling bias) arises because the endogeneity of the data influences the choices of decisions, affecting the distribution of future data to be collected and analyzed. We propose an instrumental-variable-based algorithm to correct for the bias. It obtains true parameter values and attains low (logarithmic-like) regret levels. We also prove a central limit theorem for statistical inference. To establish the theoretical properties, we develop a general technique that untangles the interdependence between data and actions.
Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas
Authors: Yubin Lu, Yang Li, Jinqiao Duan
Date: 2021-08-28 00:00:00

With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian fluctuations, the effective data-driven methods to identify stochastic differential equations with non-Gaussian L\'evy noise are relatively few so far. In this work, we propose a data-driven approach to extract stochastic governing laws with both (Gaussian) Brownian motion and (non-Gaussian) L\'evy motion, from short bursts of simulation data. Specifically, we use the normalizing flows technology to estimate the transition probability density function (solution of nonlocal Fokker-Planck equation) from data, and then substitute it into the recently proposed nonlocal Kramers-Moyal formulas to approximate L\'evy jump measure, drift coefficient and diffusion coefficient. We demonstrate that this approach can learn the stochastic differential equation with L\'evy motion. We present examples with one- and two-dimensional, decoupled and coupled systems to illustrate our method. This approach will become an effective tool for discovering stochastic governing laws and understanding complex dynamical behaviors.
Variational Inference with NoFAS: Normalizing Flow with Adaptive Surrogate for Computationally Expensive Models
Authors: Yu Wang, Fang Liu, Daniele E. Schiavazzi
Date: 2021-08-28 00:00:00
Tasks: Bayesian Inference, Variational Inference

Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable when each likelihood evaluation is computationally expensive. New approaches combining variational inference with normalizing flow are characterized by a computational cost that grows only linearly with the dimensionality of the latent variable space, and rely on gradient-based optimization instead of sampling, providing a more efficient approach for Bayesian inference about the model parameters. Moreover, the cost of frequently evaluating an expensive likelihood can be mitigated by replacing the true model with an offline trained surrogate model, such as neural networks. However, this approach might generate significant bias when the surrogate is insufficiently accurate around the posterior modes. To reduce the computational cost without sacrificing inferential accuracy, we propose Normalizing Flow with Adaptive Surrogate (NoFAS), an optimization strategy that alternatively updates the normalizing flow parameters and surrogate model parameters. We also propose an efficient sample weighting scheme for surrogate model training that preserves global accuracy while effectively capturing high posterior density regions. We demonstrate the inferential and computational superiority of NoFAS against various benchmarks, including cases where the underlying model lacks identifiability. The source code and numerical experiments used for this study are available at https://github.com/cedricwangyu/NoFAS.
Avoiding unwanted results in locally linear embedding: A new understanding of regularization
Authors: Liren Lin
Date: 2021-08-28 00:00:00

We demonstrate that locally linear embedding (LLE) inherently admits some unwanted results when no regularization is used, even for cases in which regularization is not supposed to be needed in the original algorithm. The existence of one special type of result, which we call ``projection pattern'', is mathematically proved in the situation that an exact local linear relation is achieved in each neighborhood of the data. These special patterns as well as some other bizarre results that may occur in more general situations are shown by numerical examples on the Swiss roll with a hole embedded in a high dimensional space. It is observed that all these bad results can be effectively prevented by using regularization.
Photonic Quantum Policy Learning in OpenAI Gym
Authors: Dániel Nagy, Zsolt Tabi, Péter Hága, Zsófia Kallus, Zoltán Zimborás
Date: 2021-08-29 00:00:00
Tasks: BIG-bench Machine Learning, continuous-control, Continuous Control, OpenAI Gym, Quantum Machine Learning

In recent years, near-term noisy intermediate scale quantum (NISQ) computing devices have become available. One of the most promising application areas to leverage such NISQ quantum computer prototypes is quantum machine learning. While quantum neural networks are widely studied for supervised learning, quantum reinforcement learning is still just an emerging field of this area. To solve a classical continuous control problem, we use a continuous-variable quantum machine learning approach. We introduce proximal policy optimization for photonic variational quantum agents and also study the effect of the data re-uploading. We present performance assessment via empirical study using Strawberry Fields, a photonic simulator Fock backend and a hybrid training framework connected to an OpenAI Gym environment and TensorFlow. For the restricted CartPole problem, the two variations of the photonic policy learning achieve comparable performance levels and a faster convergence than the baseline classical neural network of same number of trainable parameters.
Communication-Computation Efficient Device-Edge Co-Inference via AutoML
Authors: Xinjie Zhang, Jiawei Shao, Yuyi Mao, Jun Zhang
Date: 2021-08-30 00:00:00
Tasks: AutoML, Decoder, Deep Reinforcement Learning, Feature Compression, image-classification, Image Classification

Device-edge co-inference, which partitions a deep neural network between a resource-constrained mobile device and an edge server, recently emerges as a promising paradigm to support intelligent mobile applications. To accelerate the inference process, on-device model sparsification and intermediate feature compression are regarded as two prominent techniques. However, as the on-device model sparsity level and intermediate feature compression ratio have direct impacts on computation workload and communication overhead respectively, and both of them affect the inference accuracy, finding the optimal values of these hyper-parameters brings a major challenge due to the large search space. In this paper, we endeavor to develop an efficient algorithm to determine these hyper-parameters. By selecting a suitable model split point and a pair of encoder/decoder for the intermediate feature vector, this problem is casted as a sequential decision problem, for which, a novel automated machine learning (AutoML) framework is proposed based on deep reinforcement learning (DRL). Experiment results on an image classification task demonstrate the effectiveness of the proposed framework in achieving a better communication-computation trade-off and significant inference speedup against various baseline schemes.
An Introduction to Variational Inference
Authors: Ankush Ganguly, Samuel W. F. Earp
Date: 2021-08-30 00:00:00
Tasks: Generative Adversarial Network, Variational Inference

Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate complex probability densities. This property allows VI to converge faster than classical methods, such as, Markov Chain Monte Carlo sampling. Conceptually, VI works by choosing a family of probability density functions and then finding the one closest to the actual probability density -- often using the Kullback-Leibler (KL) divergence as the optimization metric. We introduce the Evidence Lower Bound to tractably compute the approximated probability density and we review the ideas behind mean-field variational inference. Finally, we discuss the applications of VI to variational auto-encoders (VAE) and VAE-Generative Adversarial Network (VAE-GAN). With this paper, we aim to explain the concept of VI and assist in future research with this approach.
Investigating Vulnerabilities of Deep Neural Policies
Authors: Ezgi Korkmaz
Date: 2021-08-30 00:00:00
Tasks: Deep Reinforcement Learning, reinforcement-learning, Reinforcement Learning (RL), Sensitivity

Reinforcement learning policies based on deep neural networks are vulnerable to imperceptible adversarial perturbations to their inputs, in much the same way as neural network image classifiers. Recent work has proposed several methods to improve the robustness of deep reinforcement learning agents to adversarial perturbations based on training in the presence of these imperceptible perturbations (i.e. adversarial training). In this paper, we study the effects of adversarial training on the neural policy learned by the agent. In particular, we follow two distinct parallel approaches to investigate the outcomes of adversarial training on deep neural policies based on worst-case distributional shift and feature sensitivity. For the first approach, we compare the Fourier spectrum of minimal perturbations computed for both adversarially trained and vanilla trained neural policies. Via experiments in the OpenAI Atari environments we show that minimal perturbations computed for adversarially trained policies are more focused on lower frequencies in the Fourier domain, indicating a higher sensitivity of these policies to low frequency perturbations. For the second approach, we propose a novel method to measure the feature sensitivities of deep neural policies and we compare these feature sensitivity differences in state-of-the-art adversarially trained deep neural policies and vanilla trained deep neural policies. We believe our results can be an initial step towards understanding the relationship between adversarial training and different notions of robustness for neural policies.
On the approximation of a matrix
Authors: Samriddha Sanyal
Date: 2021-08-25 00:00:00

Let $F^{*}$ be an approximation of a given $(a \times b)$ matrix $F$ derived by methods that are not randomized. We prove that for a given $F$ and $F^{*}$, $H$ and $T$ can be computed by randomized algorithm such that $(HT)$ is an approximation of $F$ better than $F^{*}$.
Representation of binary classification trees with binary features by quantum circuits
Authors: Raoul Heese, Patricia Bickert, Astrid Elisa Niederle
Date: 2021-08-30 00:00:00
Tasks: Binary Classification

We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision tree can be realized via measurements of a quantum circuit. We describe how tree inductions and the prediction of class labels of query data can be integrated into this framework. An on-demand sampling method enables predictions with a constant number of classical memory slots, independent of the tree depth. We experimentally study our approach using both a quantum computing simulator and actual IBM quantum hardware. To our knowledge, this is the first realization of a decision tree classifier on a quantum device.
On the effects of biased quantum random numbers on the initialization of artificial neural networks
Authors: Raoul Heese, Moritz Wolter, Sascha Mücke, Lukas Franken, Nico Piatkowski
Date: 2021-08-30 00:00:00

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum (NISQ) devices. A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.
Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data
Authors: Janine Witte, Ronja Foraita, Vanessa Didelez
Date: 2021-08-30 00:00:00
Tasks: Causal Discovery, Imputation, Missing Values

Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focussing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery algorithms rely on conditional independence testing when building the graph. Until recently, these algorithms have been unable to handle missing values. In this paper, we investigate two alternative solutions: Test-wise deletion and multiple imputation. We establish necessary and sufficient conditions for the recoverability of causal structures under test-wise deletion, and argue that multiple imputation is more challenging in the context of causal discovery than for estimation. We conduct an extensive comparison by simulating from benchmark causal graphs: As one might expect, we find that test-wise deletion and multiple imputation both clearly outperform list-wise deletion and single imputation. Crucially, our results further suggest that multiple imputation is especially useful in settings with a small number of either Gaussian or discrete variables, but when the dataset contains a mix of both neither method is uniformly best. The methods we compare include random forest imputation and a hybrid procedure combining test-wise deletion and multiple imputation. An application to data from the IDEFICS cohort study on diet- and lifestyle-related diseases in European children serves as an illustrating example.
Survival Prediction of Heart Failure Patients using Stacked Ensemble Machine Learning Algorithm
Authors: S. M Mehedi Zaman, Wasay Mahmood Qureshi, Md. Mohsin Sarker Raihan, Ocean Monjur, Abdullah Bin Shams
Date: 2021-08-30 00:00:00
Tasks: BIG-bench Machine Learning, Ensemble Learning, Survival Prediction

Cardiovascular disease, especially heart failure is one of the major health hazard issues of our time and is a leading cause of death worldwide. Advancement in data mining techniques using machine learning (ML) models is paving promising prediction approaches. Data mining is the process of converting massive volumes of raw data created by the healthcare institutions into meaningful information that can aid in making predictions and crucial decisions. Collecting various follow-up data from patients who have had heart failures, analyzing those data, and utilizing several ML models to predict the survival possibility of cardiovascular patients is the key aim of this study. Due to the imbalance of the classes in the dataset, Synthetic Minority Oversampling Technique (SMOTE) has been implemented. Two unsupervised models (K-Means and Fuzzy C-Means clustering) and three supervised classifiers (Random Forest, XGBoost and Decision Tree) have been used in our study. After thorough investigation, our results demonstrate a superior performance of the supervised ML algorithms over unsupervised models. Moreover, we designed and propose a supervised stacked ensemble learning model that can achieve an accuracy, precision, recall and F1 score of 99.98%. Our study shows that only certain attributes collected from the patients are imperative to successfully predict the surviving possibility post heart failure, using supervised ML algorithms.