Fractal interpolation in the context of prediction accuracy optimization

• URL: http://arxiv.org/abs/2403.00403v1
• Date: Fri, 1 Mar 2024 09:49:53 GMT
• Title: Fractal interpolation in the context of prediction accuracy optimization
• Authors: Alexandra Baicoianu, Cristina Gabriela Gavril\u{a}, Cristina Maria Pacurar, Victor Dan Pacurar
• Abstract summary: This paper focuses on the hypothesis of optimizing time series predictions using fractal techniques. Prediction results obtained with the LSTM model showed a significant accuracy improvement compared to the raw datasets.
• Score: 44.99833362998488
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper focuses on the hypothesis of optimizing time series predictions using fractal interpolation techniques. In general, the accuracy of machine learning model predictions is closely related to the quality and quantitative aspects of the data used, following the principle of \textit{garbage-in, garbage-out}. In order to quantitatively and qualitatively augment datasets, one of the most prevalent concerns of data scientists is to generate synthetic data, which should follow as closely as possible the actual pattern of the original data. This study proposes three different data augmentation strategies based on fractal interpolation, namely the \textit{Closest Hurst Strategy}, \textit{Closest Values Strategy} and \textit{Formula Strategy}. To validate the strategies, we used four public datasets from the literature, as well as a private dataset obtained from meteorological records in the city of Brasov, Romania. The prediction results obtained with the LSTM model using the presented interpolation strategies showed a significant accuracy improvement compared to the raw datasets, thus providing a possible answer to practical problems in the field of remote sensing and sensor sensitivity. Moreover, our methodologies answer some optimization-related open questions for the fractal interpolation step using \textit{Optuna} framework.

Related papers

• DUPRE: Data Utility Prediction for Efficient Data Valuation [49.60564885180563]
  Cooperative game theory-based data valuation, such as Data Shapley, requires evaluating the data utility and retraining the ML model for multiple data subsets. Our framework, textttDUPRE, takes an alternative yet complementary approach that reduces the cost per subset evaluation by predicting data utilities instead of evaluating them by model retraining. Specifically, given the evaluated data utilities of some data subsets, textttDUPRE fits a emphGaussian process (GP) regression model to predict the utility of every other data subset.
  arXiv  Detail & Related papers  (2025-02-22T08:53:39Z)
• TD3: Tucker Decomposition Based Dataset Distillation Method for Sequential Recommendation [50.23504065567638]
  This paper introduces textbfTD3, a novel textbfDataset textbfDistillation method within a meta-learning framework. TD3 distills a fully expressive emphsynthetic sequence summary from original data. An augmentation technique allows the learner to closely fit the synthetic summary, ensuring an accurate update of it in the emphouter-loop.
  arXiv  Detail & Related papers  (2025-02-05T03:13:25Z)
• Kriging and Gaussian Process Interpolation for Georeferenced Data Augmentation [10.945947159224302]
  This study explores techniques for the augmentation of geo-referenced data, with the aim of predicting the presence of Commelina benghalensis L. in sugarcane plots in La R'eunion. Given the spatial nature of the data and the high cost of collection data, we evaluated two approaches: Gaussian processes (GPs) with different kernels and kriging with various variograms. The results show that GP-based methods, in particular with combined kernels (GP-COMB), significantly improve the performance of regression algorithms while requiring less additional data.
  arXiv  Detail & Related papers  (2025-01-13T10:29:09Z)
• Interpolation pour l'augmentation de donnees : Application à la gestion des adventices de la canne a sucre a la Reunion [10.945947159224302]
  This study explores techniques for the augmentation of geo-referenced data. The aim is to predict the presence of Commelina benghalensis L. in sugarcane plots in La R'eunion.
  arXiv  Detail & Related papers  (2025-01-10T11:02:13Z)
• Transfer Learning in $\ell_1$ Regularized Regression: Hyperparameter Selection Strategy based on Sharp Asymptotic Analysis [3.5374094795720854]
  Transfer learning techniques aim to leverage information from multiple related datasets to enhance prediction quality against a target dataset. Some Lasso-based algorithms have been invented: Trans-Lasso and Pretraining Lasso. We conduct a thorough, precise study of the algorithm in a high-dimensional setting via an analysis using the replica method. Our approach reveals a surprisingly simple behavior of the algorithm: Ignoring one of the two types of information transferred to the fine-tuning stage has little effect on generalization performance.
  arXiv  Detail & Related papers  (2024-09-26T10:20:59Z)
• Ranking and Combining Latent Structured Predictive Scores without Labeled Data [2.5064967708371553]
  This paper introduces a novel structured unsupervised ensemble learning model (SUEL) It exploits the dependency between a set of predictors with continuous predictive scores, rank the predictors without labeled data and combine them to an ensembled score with weights. The efficacy of the proposed methods is rigorously assessed through both simulation studies and real-world application of risk genes discovery.
  arXiv  Detail & Related papers  (2024-08-14T20:14:42Z)
• Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets [11.105392318582677]
  We propose a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure. We show that in a high-dimensional regime, the EOT plan recovers the shared manifold structure by approximating a kernel function evaluated at the locations of the latent variables.
  arXiv  Detail & Related papers  (2024-07-01T18:48:55Z)
• Hierarchical Features Matter: A Deep Exploration of GAN Priors for Improved Dataset Distillation [51.44054828384487]
  We propose a novel parameterization method dubbed Hierarchical Generative Latent Distillation (H-GLaD) This method systematically explores hierarchical layers within the generative adversarial networks (GANs) In addition, we introduce a novel class-relevant feature distance metric to alleviate the computational burden associated with synthetic dataset evaluation.
  arXiv  Detail & Related papers  (2024-06-09T09:15:54Z)
• Minimally Supervised Learning using Topological Projections in Self-Organizing Maps [55.31182147885694]
  We introduce a semi-supervised learning approach based on topological projections in self-organizing maps (SOMs) Our proposed method first trains SOMs on unlabeled data and then a minimal number of available labeled data points are assigned to key best matching units (BMU) Our results indicate that the proposed minimally supervised model significantly outperforms traditional regression techniques.
  arXiv  Detail & Related papers  (2024-01-12T22:51:48Z)
• Large-scale Fully-Unsupervised Re-Identification [78.47108158030213]
  We propose two strategies to learn from large-scale unlabeled data. The first strategy performs a local neighborhood sampling to reduce the dataset size in each without violating neighborhood relationships. A second strategy leverages a novel Re-Ranking technique, which has a lower time upper bound complexity and reduces the memory complexity from O(n2) to O(kn) with k n.
  arXiv  Detail & Related papers  (2023-07-26T16:19:19Z)
• A Hybrid Framework for Sequential Data Prediction with End-to-End Optimization [0.0]
  We investigate nonlinear prediction in an online setting and introduce a hybrid model that effectively mitigates hand-designed features and manual model selection issues. We employ a recurrent neural network (LSTM) for adaptive feature extraction from sequential data and a gradient boosting machinery (soft GBDT) for effective supervised regression. We demonstrate the learning behavior of our algorithm on synthetic data and the significant performance improvements over the conventional methods over various real life datasets.
  arXiv  Detail & Related papers  (2022-03-25T17:13:08Z)
• CAFE: Learning to Condense Dataset by Aligning Features [72.99394941348757]
  We propose a novel scheme to Condense dataset by Aligning FEatures (CAFE) At the heart of our approach is an effective strategy to align features from the real and synthetic data across various scales. We validate the proposed CAFE across various datasets, and demonstrate that it generally outperforms the state of the art.
  arXiv  Detail & Related papers  (2022-03-03T05:58:49Z)
• Riemannian classification of EEG signals with missing values [67.90148548467762]
  This paper proposes two strategies to handle missing data for the classification of electroencephalograms. The first approach estimates the covariance from imputed data with the $k$-nearest neighbors algorithm; the second relies on the observed data by leveraging the observed-data likelihood within an expectation-maximization algorithm. As results show, the proposed strategies perform better than the classification based on observed data and allow to keep a high accuracy even when the missing data ratio increases.
  arXiv  Detail & Related papers  (2021-10-19T14:24:50Z)
• Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition [18.07071669486882]
  We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions. We formulate the relationship between the latent positions and the observed data via a generalized multilinear kernel as the link function. We demonstrate the effectiveness of our method on synthetic data.
  arXiv  Detail & Related papers  (2021-06-30T13:11:17Z)
• Hierarchical regularization networks for sparsification based learning on noisy datasets [0.0]
  hierarchy follows from approximation spaces identified at successively finer scales. For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension. Results show the performance of the approach as a data reduction and modeling strategy on both synthetic and real datasets.
  arXiv  Detail & Related papers  (2020-06-09T18:32:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.