Dimensionality reduction to maximize prediction generalization capability

• URL: http://arxiv.org/abs/2003.00470v2
• Date: Thu, 20 Jan 2022 08:48:42 GMT
• Title: Dimensionality reduction to maximize prediction generalization capability
• Authors: Takuya Isomura, Taro Toyoizumi
• Abstract summary: Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme that extracts the most informative components for predicting future inputs, termed predictive principal component analysis (PredPCA) Our scheme can effectively remove unpredictable noise and minimize test prediction error through convex optimization.
• Score: 0.7614628596146599
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme that extracts the most informative components for predicting future inputs, termed predictive principal component analysis (PredPCA). Our scheme can effectively remove unpredictable noise and minimize test prediction error through convex optimization. Mathematical analyses demonstrate that, provided with sufficient training samples and sufficiently high-dimensional observations, PredPCA can asymptotically identify hidden states, system parameters, and dimensionalities of canonical nonlinear generative processes, with a global convergence guarantee. We demonstrate the performance of PredPCA using sequential visual inputs comprising hand-digits, rotating 3D objects, and natural scenes. It reliably estimates distinct hidden states and predicts future outcomes of previously unseen test input data, based exclusively on noisy observations. The simple architecture and low computational cost of PredPCA are highly desirable for neuromorphic hardware.

Related papers

• LMD: Light-weight Prediction Quality Estimation for Object Detection in Lidar Point Clouds [3.927702899922668]
  Object detection on Lidar point cloud data is a promising technology for autonomous driving and robotics. Uncertainty estimation is a crucial component for down-stream tasks and deep neural networks remain error-prone even for predictions with high confidence. We propose LidarMetaDetect, a light-weight post-processing scheme for prediction quality estimation. Our experiments show a significant increase of statistical reliability in separating true from false predictions.
  arXiv  Detail & Related papers  (2023-06-13T15:13:29Z)
• Variational Inference with Coverage Guarantees in Simulation-Based Inference [18.818573945984873]
  We propose Conformalized Amortized Neural Variational Inference (CANVI) CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation.
  arXiv  Detail & Related papers  (2023-05-23T17:24:04Z)
• Prediction-Powered Inference [68.97619568620709]
  Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing provably valid confidence intervals for quantities such as means, quantiles, and linear and logistic regression coefficients. Prediction-powered inference could enable researchers to draw valid and more data-efficient conclusions using machine learning.
  arXiv  Detail & Related papers  (2023-01-23T18:59:28Z)
• Deep Subspace Encoders for Nonlinear System Identification [0.0]
  We propose a method which uses a truncated prediction loss and a subspace encoder for state estimation. We show that, under mild conditions, the proposed method is locally consistent, increases optimization stability, and achieves increased data efficiency.
  arXiv  Detail & Related papers  (2022-10-26T16:04:38Z)
• Efficient and Differentiable Conformal Prediction with General Function Classes [96.74055810115456]
  We propose a generalization of conformal prediction to multiple learnable parameters. We show that it achieves approximate valid population coverage and near-optimal efficiency within class. Experiments show that our algorithm is able to learn valid prediction sets and improve the efficiency significantly.
  arXiv  Detail & Related papers  (2022-02-22T18:37:23Z)
• A Method for Controlling Extrapolation when Visualizing and Optimizing the Prediction Profiles of Statistical and Machine Learning Models [0.0]
  We present a novel method for controlling extrapolation in the prediction profiler in the JMP software. Our method helps users avoid exploring predictions that should be considered extrapolation.
  arXiv  Detail & Related papers  (2022-01-13T22:31:32Z)
• Imputation-Free Learning from Incomplete Observations [73.15386629370111]
  We introduce the importance of guided gradient descent (IGSGD) method to train inference from inputs containing missing values without imputation. We employ reinforcement learning (RL) to adjust the gradients used to train the models via back-propagation. Our imputation-free predictions outperform the traditional two-step imputation-based predictions using state-of-the-art imputation methods.
  arXiv  Detail & Related papers  (2021-07-05T12:44:39Z)
• Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression [51.770998056563094]
  Probabilistic Gradient Boosting Machines (PGBM) is a method to create probabilistic predictions with a single ensemble of decision trees. We empirically demonstrate the advantages of PGBM compared to existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-03T08:32:13Z)
• Representation Learning for Sequence Data with Deep Autoencoding Predictive Components [96.42805872177067]
  We propose a self-supervised representation learning method for sequence data, based on the intuition that useful representations of sequence data should exhibit a simple structure in the latent space. We encourage this latent structure by maximizing an estimate of predictive information of latent feature sequences, which is the mutual information between past and future windows at each time step. We demonstrate that our method recovers the latent space of noisy dynamical systems, extracts predictive features for forecasting tasks, and improves automatic speech recognition when used to pretrain the encoder on large amounts of unlabeled data.
  arXiv  Detail & Related papers  (2020-10-07T03:34:01Z)
• Learning Output Embeddings in Structured Prediction [73.99064151691597]
  A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension. A prediction in the original space is computed by solving a pre-image problem. In this work, we propose to jointly learn a finite approximation of the output embedding and the regression function into the new feature space.
  arXiv  Detail & Related papers  (2020-07-29T09:32:53Z)

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.