We introduce Sparse Symplectically Integrated Neural Networks (SSINNs), a novel model for learning Hamiltonian dynamical systems from data. SSINNs combine fourth-order symplectic integration with a learned parameterization of the Hamiltonian obtained using sparse regression through a mathematically elegant function space. This allows for interpretable models that incorporate symplectic inductive biases and have low memory requirements. We evaluate SSINNs on four classical Hamiltonian dynamical problems: the Hénon-Heiles system, nonlinearly coupled oscillators, a multi-particle mass-spring system, and a pendulum system. Our results demonstrate promise in both system prediction and conservation of energy, often outperforming the current state-of-the-art black-box prediction techniques by an order of magnitude. Further, SSINNs successfully converge to true governing equations from highly limited and noisy data, demonstrating potential applicability in the discovery of new physical governing equations.
Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to probabilistically sample Hamiltonian symbolic expressions. Using symplectic neural networks, we develop a model-agnostic approach for extracting meaningful physical priors from the data that can be imposed on-the-fly into the RNN output, limiting its search space. Hamiltonians generated by the RNN are optimized and assessed using a fourth-order symplectic integ…
In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational c…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration method named Integrated Principal Components Analysis (iPCA), which is a model-based generalization of PCA and serves as a practical tool to find and visualize common patterns that occur in multiple data sets. The key idea driving iPCA is the matrix-variate normal model, whose Kronecker product covariance structure captures both individual patterns within each …
Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning (SGL), for variable selection and dimension reduction via learning the gradients of the prediction function directly from samples. By imposing a sparsity constraint on the gradients, variable selection is achieved by selecting variables corresponding to non-zero partial derivatives, and effective dimensions are extracted based on the eigenvectors of the derived s…
The high-dimensionality and volume of large scale multistream data has inhibited significant research progress in developing an integrated monitoring and diagnostics (M&D) approach. This data, also categorized as big data, is becoming common in manufacturing plants. In this paper, we propose an integrated M\&D approach for large scale streaming data. We developed a novel monitoring method named Adaptive Principal Component monitoring (APC) which adaptively chooses PCs that are most likely to vary due to the change for early detection. Importantly, we integrate a novel diagnostic approach, Prin…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in sparsity-related techniques. We cast the problem, resembling group or collaborative sparsity formulations, as a non-smooth convex optimization problem that can be efficiently solved using augmented Lagrangian techniques. The method can deal with weighted or unweighted graphs, as well as multimodal data, where different graphs represent different types of data. The propose…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm scalability and model interpretability are difficult to achieve, not to mention the prevalence of missing values. While existing sparse PCA methods alleviate inconsistency, they are constrained to the Gaussian assumption of classical PCA and fail to address algorithm scalability issues. We generalize sparse PCA to the broad exponential family distributions under high-…
This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a double-detector scheme is introduced in which a sensor level threshold detector is integrated into network level GLRT to improve the performance. The detection criteria of oracle and clairvoyant detectors are also derived. Simulation results show that with careful design of the t…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted for. In past decades, the vast majority of robust linear regression estimators has focused on robustness against rowwise contamination. Even so called `high breakdown' estimators rely on the assumption that a majority of rows of the regression matrix is not affected by outliers. Only very recently, the first cellwise robust regression estimation methods hav…
We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from previous studies or genomic databases, and information borrowed across a set of genes or genomic networks. The approach is based on prior modelling of the regression parameters using the horseshoe prior, with a prior on the sparsity index that depends on external information. Multiple datasets are integrated by applying an empirical Bayes strategy on hyperparameter…
College of Economics and Management, Shandong University of Science and Technology（山东科技大学经济管理学院）
We propose a novel filter for sparse big data, called an integrated autoencoder (IAE), which utilizes auxiliary information to mitigate data sparsity. The proposed model achieves an appropriate balance between prediction accuracy, convergence speed, and complexity. We implement experiments on a GPS trajectory dataset, and the results demonstrate that the IAE is more accurate and robust than some state-of-the-art methods.
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional sparse data, however, the method suffers from slow convergence and high variance due to the heterogeneity in feature sparsity. To mitigate this issue, we introduce a stabilized truncated stochastic gradient descent algorithm. We employ a soft-thresholding scheme on the weight vector where the imposed shrinkage is adaptive to the amount of information availab…
Georgia Institute of Technology（佐治亚理工学院）；Intel Labs（英特尔研究院）
Deep Learning (DL) acceleration support in CPUs has recently gained a lot of traction, with several companies (Arm, Intel, IBM) announcing products with specialized matrix engines accessible via GEMM instructions. CPUs are pervasive and need to handle diverse requirements across DL workloads running in edge/HPC/cloud platforms. Therefore, as DL workloads embrace sparsity to reduce the computations and memory size of models, it is also imperative for CPUs to add support for sparsity to avoid under-utilization of the dense matrix engine and inefficient usage of the caches and registers. This wor…
This paper introduces an elemental building block which combines Dictionary Learning and Dimension Reduction (DRDL). We show how this foundational element can be used to iteratively construct a Hierarchical Sparse Representation (HSR) of a sensory stream. We compare our approach to existing models showing the generality of our simple prescription. We then perform preliminary experiments using this framework, illustrating with the example of an object recognition task using standard datasets. This work introduces the very first steps towards an integrated framework for designing and analyzing v…
We consider high-dimensional distribution estimation through autoregressive networks. By combining the concepts of sparsity, mixtures and parameter sharing we obtain a simple model which is fast to train and which achieves state-of-the-art or better results on several standard benchmark datasets. Specifically, we use an L1-penalty to regularize the conditional distributions and introduce a procedure for automatic parameter sharing between mixture components. Moreover, we propose a simple distributed representation which permits exact likelihood evaluations since the latent variables are interl…
Computer Science and Engineering, Arizona State University, USA（亚利桑那州立大学计算机科学与工程学院，美国）；SAS Institute Inc., USA（美国SAS研究所）
The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper, we present a fast and effective sparse logistic regression screening rule (Slores) to identify the 0 components in the solution vector, which may lead to a substantial reduction in the number of features to be entered to the optimization. An appealing feature of Slores is that …
A general physics-constrained method for the modelling of equation's closure terms with sparse data
Institute of Applied Physics and Computational Mathematics, Beijing（应用物理与计算数学研究院）；Graduate School of China Academy of Engineering Physics, Beijing（中国工程物理研究院研究生院）；National Key Laboratory of Computational Physics（计算物理国家重点实验室）
Yale University（耶鲁大学）；Indian Institute of Technology, Delhi（印度理工学院德里分校）
Recently several structured pruning techniques have been introduced for energy-efficient implementation of Deep Neural Networks (DNNs) with lesser number of crossbars. Although, these techniques have claimed to preserve the accuracy of the sparse DNNs on crossbars, none have studied the impact of the inexorable crossbar non-idealities on the actual performance of the pruned networks. To this end, we perform a comprehensive study to show how highly sparse DNNs, that result in significant crossbar-compression-rate, can lead to severe accuracy losses compared to unpruned DNNs mapped onto non-idea…
Link prediction on dynamic graphs is an important task in graph mining. Existing approaches based on dynamic graph neural networks (DGNNs) typically require a significant amount of historical data (interactions over time), which is not always available in practice. The missing links over time, which is a common phenomenon in graph data, further aggravates the issue and thus creates extremely sparse and dynamic graphs. To address this problem, we propose a novel method based on the neural process, called Graph Sequential Neural ODE Process (GSNOP). Specifically, GSNOP combines the advantage of …
The recently proposed multi-layer sparse model has raised insightful connections between sparse representations and convolutional neural networks (CNN). In its original conception, this model was restricted to a cascade of convolutional synthesis representations. In this paper, we start by addressing a more general model, revealing interesting ties to fully connected networks. We then show that this multi-layer construction admits a brand new interpretation in a unique symbiosis between synthesis and analysis models: while the deepest layer indeed provides a synthesis representation, the mid-l…
