Tensor-Train Networks for Learning Predictive Modeling of Multidimensional Data
In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor model and standard multilayer neural networks is also carried out in the context of prediction of the Mackey-Glass noisy chaotic time series and NASDAQ index. We show that the weights of a multidimensional regression model can be learned by means of TT network and the optimization of TT weights is a more robust to the impact of coefficient initialization and hyper-parameter setting. Furthermore, an efficient algorithm based on alternating least squares has been proposed for approximating the weights in TT-format with a reduction of computational calculus, providing a much faster convergence than the well-known adaptive learning-method algorithms, widely applied for optimizing neural networks.
Code (0)
등록된 구현이 없습니다.
Tasks
Tensor NetworksTime SeriesTime Series AnalysisSimilar Papers 제목 키워드 기반
DinTucker: Scaling up Gaussian process models on multidimensional arrays with billions of elements
Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods in…
Tensor DecompositionVariational InferenceTensor-Valued Time and Inference Path Optimization in Differential Equation-Based Generative Modeling
In the field of generative modeling based on differential equations, conventional methods utilize scalar-valued time during both the training and inference phases. This work introduces, for the first time, a tensor-value…
Money as a Tensor
The proposed framework introduces a novel multidimensional representation of money using tensor analysis, enabling a more granular examination of economic interactions and capital flow. By treating money as a multidimens…
Decision MakingGuaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory
In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to pres…
Computational EfficiencyPredictionTensor DecompositionTime Series+1Multilinear Dynamical Systems for Tensor Time Series
Many scientific data occur as sequences of multidimensional arrays called tensors. How can hidden, evolving trends in such data be extracted while preserving the tensor structure? The model that is traditionally used i…
Time SeriesTime Series Analysis