scholarly journals Sparse quantum Gaussian processes to counter the curse of dimensionality

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Gaweł I. Kuś ◽  
Sybrand van der Zwaag ◽  
Miguel A. Bessa
Keyword(s):  
Machine Learning ◽  
Quantum Computing ◽  
Gaussian Processes ◽  
Complexity Analysis ◽  
Input Parameter ◽  
Computational Cost ◽  
Curse Of Dimensionality ◽  
Machine Learning Algorithms ◽  
Low Rank ◽  
Low Rank Approximation

AbstractGaussian processes are well-established Bayesian machine learning algorithms with significant merits, despite a strong limitation: lack of scalability. Clever solutions address this issue by inducing sparsity through low-rank approximations, often based on the Nystrom method. Here, we propose a different method to achieve better scalability and higher accuracy using quantum computing, outperforming classical Bayesian neural networks for large datasets significantly. Unlike other approaches to quantum machine learning, the computationally expensive linear algebra operations are not just replaced with their quantum counterparts. Instead, we start from a recent study that proposed a quantum circuit for implementing quantum Gaussian processes and then we use quantum phase estimation to induce a low-rank approximation analogous to that in classical sparse Gaussian processes. We provide evidence through numerical tests, mathematical error bound estimation, and complexity analysis that the method can address the “curse of dimensionality,” where each additional input parameter no longer leads to an exponential growth of the computational cost. This is also demonstrated by applying the algorithm in a practical setting and using it in the data-driven design of a recently proposed metamaterial. The algorithm, however, requires significant quantum computing hardware improvements before quantum advantage can be achieved.

scholarly journals Smooth input preparation for quantum and quantum-inspired machine learning

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhikuan Zhao ◽  
Jack K. Fitzsimons ◽  
Patrick Rebentrost ◽  
Vedran Dunjko ◽  
Joseph F. Fitzsimons
Keyword(s):  
Machine Learning ◽  
Quantum Algorithms ◽  
Machine Learning Algorithms ◽  
Low Rank ◽  
Smoothed Analysis ◽  
Machine Learning Applications ◽  
Data Points ◽  
Input Model ◽  
The Cost ◽  
Input Perturbation

AbstractMachine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum-enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states proportional to high-dimensional data points stored in a quantum accessible memory. Even given query access to exponentially many entries stored in a database, the construction of which is considered a one-off overhead, it has been argued that the cost of preparing such amplitude-encoded states may offset any exponential quantum advantage. Here we prove using smoothed analysis that if the data analysis algorithm is robust against small entry-wise input perturbation, state preparation can always be achieved with constant queries. This criterion is typically satisfied in realistic machine learning applications, where input data is subjective to moderate noise. Our results are equally applicable to the recent seminal progress in quantum-inspired algorithms, where specially constructed databases suffice for polylogarithmic classical algorithm in low-rank cases. The consequence of our finding is that for the purpose of practical machine learning, polylogarithmic processing time is possible under a general and flexible input model with quantum algorithms or quantum-inspired classical algorithms in the low-rank cases.

Recent Progress in Quantum Machine Learning

2021 ◽  
pp. 232-256
Author(s):  
Amandeep Singh Bhatia ◽  
Renata Wong
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Quantum Computing ◽  
Recent Progress ◽  
Machine Learning Algorithms ◽  
Learning Models ◽  
Exciting Field ◽  
Quantum Machine Learning ◽  
The Subject ◽  
Machine Learning Models

Quantum computing is a new exciting field which can be exploited to great speed and innovation in machine learning and artificial intelligence. Quantum machine learning at crossroads explores the interaction between quantum computing and machine learning, supplementing each other to create models and also to accelerate existing machine learning models predicting better and accurate classifications. The main purpose is to explore methods, concepts, theories, and algorithms that focus and utilize quantum computing features such as superposition and entanglement to enhance the abilities of machine learning computations enormously faster. It is a natural goal to study the present and future quantum technologies with machine learning that can enhance the existing classical algorithms. The objective of this chapter is to facilitate the reader to grasp the key components involved in the field to be able to understand the essentialities of the subject and thus can compare computations of quantum computing with its counterpart classical machine learning algorithms.

Comparison of Machine Learning Algorithms in the Interpolation and Extrapolation of Flame Describing Functions

2019 ◽  
Author(s):  
Michael McCartney ◽  
Matthias Haeringer ◽  
Wolfgang Polifke
Keyword(s):  
Machine Learning ◽  
Gaussian Processes ◽  
Spline Interpolation ◽  
Learning Algorithms ◽  
Predictive Performance ◽  
Machine Learning Algorithms ◽  
Test Time ◽  
Minimal Amount ◽  
Data Points ◽  
The Impact

Abstract This paper examines and compares commonly used Machine Learning algorithms in their performance in interpolation and extrapolation of FDFs, based on experimental and simulation data. Algorithm performance is evaluated by interpolating and extrapolating FDFs and then the impact of errors on the limit cycle amplitudes are evaluated using the xFDF framework. The best algorithms in interpolation and extrapolation were found to be the widely used cubic spline interpolation, as well as the Gaussian Processes regressor. The data itself was found to be an important factor in defining the predictive performance of a model, therefore a method of optimally selecting data points at test time using Gaussian Processes was demonstrated. The aim of this is to allow a minimal amount of data points to be collected while still providing enough information to model the FDF accurately. The extrapolation performance was shown to decay very quickly with distance from the domain and so emphasis should be put on selecting measurement points in order to expand the covered domain. Gaussian Processes also give an indication of confidence on its predictions and is used to carry out uncertainty quantification, in order to understand model sensitivities. This was demonstrated through application to the xFDF framework.

Machine Learning Algorithms in Quantum Computing: A Survey

2020 ◽  
Author(s):  
Somayeh Bakhtiari Ramezani ◽  
Alexander Sommers ◽  
Harish Kumar Manchukonda ◽  
Shahram Rahimi ◽  
Amin Amirlatifi
Keyword(s):  
Machine Learning ◽  
Quantum Computing ◽  
Learning Algorithms ◽  
Machine Learning Algorithms

scholarly journals Signal-piloted processing and machine learning based efficient power quality disturbances recognition

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0252104
Author(s):  
Saeed Mian Qaisar
Keyword(s):  
Machine Learning ◽  
Power Quality ◽  
Data Storage ◽  
Computational Cost ◽  
Machine Learning Algorithms ◽  
Support Vector ◽  
K Nearest Neighbor ◽  
Processing Load ◽  
Suggested Approach ◽  
Power Quality Disturbances

Significant losses can occur for various smart grid stake holders due to the Power Quality Disturbances (PQDs). Therefore, it is necessary to correctly recognize and timely mitigate the PQDs. In this context, an emerging trend is the development of machine learning assisted PQDs management. Based on the conventional processing theory, the existing PQDs identification is time-invariant. It can result in a huge amount of unnecessary information being collected, processed, and transmitted. Consequently, needless processing activities, power consumption and latency can occur. In this paper, a novel combination of signal-piloted acquisition, adaptive-rate segmentation and time-domain features extraction with machine learning tools is suggested. The signal-piloted acquisition and processing brings real-time compression. Therefore, a remarkable reduction can be secured in the data storage, processing and transmission requirement towards the post classifier. Additionally, a reduced computational cost and latency of classifier is promised. The classification is accomplished by using robust machine learning algorithms. A comparison is made among the k-Nearest Neighbor, Naïve Bayes, Artificial Neural Network and Support Vector Machine. Multiple metrics are used to test the success of classification. It permits to avoid any biasness of findings. The applicability of the suggested approach is studied for automated recognition of the power signal’s major voltage and transient disturbances. Results show that the system attains a 6.75-fold reduction in the collected information and the processing load and secures the 98.05% accuracy of classification.

scholarly journals Machine Learning: A Quantum Perspective

2021 ◽  
Author(s):  
Aishwarya Jhanwar ◽  
Manisha J. Nene
Keyword(s):  
Machine Learning ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Quantum Computers ◽  
Learning Tasks ◽  
Current Scenario ◽  
Chip Fabrication ◽  
Classical Computing

Recently, increased availability of the data has led to advances in the field of machine learning. Despite of the growth in the domain of machine learning, the proximity to the physical limits of chip fabrication in classical computing is motivating researchers to explore the properties of quantum computing. Since quantum computers leverages the properties of quantum mechanics, it carries the ability to surpass classical computers in machine learning tasks. The study in this paper contributes in enabling researchers to understand how quantum computers can bring a paradigm shift in the field of machine learning. This paper addresses the concepts of quantum computing which influences machine learning in a quantum world. It also states the speedup observed in different machine learning algorithms when executed on quantum computers. The paper towards the end advocates the use of quantum application software and throw light on the existing challenges faced by quantum computers in the current scenario.

scholarly journals Fast and Effective Techniques for LWIR Radiative Transfer Modeling: A Dimension Reduction Approach

2019 ◽  
Author(s):  
Nicholas Westing ◽  
Brett Borghetti ◽  
Kevin Gross
Keyword(s):  
Machine Learning ◽  
Radiative Transfer ◽  
Dimension Reduction ◽  
Real Time ◽  
Computational Cost ◽  
Hyperspectral Data ◽  
Machine Learning Algorithms ◽  
Atmospheric Effects ◽  
Atmospheric Compensation ◽  
The Impact

The increasing spatial and spectral resolution of hyperspectral imagers yields detailed spectroscopy measurements from both space-based and airborne platforms. Machine learning algorithms have achieved state-of-the-art material classification performance on benchmark hyperspectral data sets; however, these techniques often do not consider varying atmospheric conditions experienced in a real-world detection scenario. To reduce the impact of atmospheric effects in the at-sensor signal, atmospheric compensation must be performed. Radiative Transfer (RT) modeling can generate high-fidelity atmospheric estimates at detailed spectral resolutions, but is often too time-consuming for real-time detection scenarios. This research utilizes machine learning methods to perform dimension reduction on the transmittance, upwelling radiance, and downwelling radiance (TUD) data to create high accuracy atmospheric estimates with lower computational cost than RT modeling. The utility of this approach is investigated using the instrument line shape for the Mako long-wave infrared hyperspectral sensor. This study employs physics-based metrics and loss functions to identify promising dimension reduction techniques. As a result, TUD vectors can be produced in real-time allowing for atmospheric compensation across diverse remote sensing scenarios.

scholarly journals Fast, accurate, and transferable many-body interatomic potentials by symbolic regression

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Alberto Hernandez ◽  
Adarsh Balasubramanian ◽  
Fenglin Yuan ◽  
Simon A. M. Mason ◽  
Tim Mueller
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Computational Cost ◽  
Symbolic Regression ◽  
Machine Learning Algorithms ◽  
Training Data ◽  
Many Body ◽  
Potential Models ◽  
Embedded Atom ◽  
Hypothesis Space

AbstractThe length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine-learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine-learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient many-body potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton-Chen embedded-atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded-atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed.

scholarly journals Robust subspace methods for outlier detection in genomic data circumvents the curse of dimensionality

2020 ◽  
Vol 7 (2) ◽  
pp. 190714 ◽  
Author(s):  
Omar Shetta ◽  
Mahesan Niranjan
Keyword(s):  
Outlier Detection ◽  
Genomic Data ◽  
Graph Laplacian ◽  
Curse Of Dimensionality ◽  
Low Rank ◽  
Learning Problems ◽  
Low Rank Approximation ◽  
Inference Problems ◽  
Reduction Techniques ◽  
Low Dimensional

The application of machine learning to inference problems in biology is dominated by supervised learning problems of regression and classification, and unsupervised learning problems of clustering and variants of low-dimensional projections for visualization. A class of problems that have not gained much attention is detecting outliers in datasets, arising from reasons such as gross experimental, reporting or labelling errors. These could also be small parts of a dataset that are functionally distinct from the majority of a population. Outlier data are often identified by considering the probability density of normal data and comparing data likelihoods against some threshold. This classical approach suffers from the curse of dimensionality, which is a serious problem with omics data which are often found in very high dimensions. We develop an outlier detection method based on structured low-rank approximation methods. The objective function includes a regularizer based on neighbourhood information captured in the graph Laplacian. Results on publicly available genomic data show that our method robustly detects outliers whereas a density-based method fails even at moderate dimensions. Moreover, we show that our method has better clustering and visualization performance on the recovered low-dimensional projection when compared with popular dimensionality reduction techniques.

scholarly journals Machine Learning for Modeling the Singular Multi-Pantograph Equations

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1041
Author(s):  
Amirhosein Mosavi ◽  
Manouchehr Shokri ◽  
Zulkefli Mansor ◽  
Sultan Noman Qasem ◽  
Shahab S. Band ◽  
...  
Keyword(s):  
Machine Learning ◽  
Fuzzy Logic ◽  
Intelligent Systems ◽  
Estimation Error ◽  
Computational Cost ◽  
Accurate Solution ◽  
Machine Learning Algorithms ◽  
Novel Approach ◽  
Cubature Kalman Filter

In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost.

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