We introduce a novel Bayesian hybrid matrix factorisation model (HMF) for data integration, based on combining multiple matrix factorisation methods, that can be used for in- and out-of-matrix prediction of missing values. The model is very general and can be used to integrate many datasets across different entity type…
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48 results for “matrix prediction”
New method predicts binary matrix entries using empirical Bayes and low-rank structure.
problem Predicting unobserved entries in binary matrices.
method Empirical Bayes method motivated by Efron--Morris estimator, exploiting low-rank structure.
result Superior performance in predictive accuracy, calibration, and efficiency compared to existing methods.
A regression algorithm uses Green's function and covariance matrix for predictive distributions.
problem Regression and uncertainty quantification for machine learning.
method Green's function theory, Bayesian approach, covariance matrix of normalized Green's function.
result The covariance matrix provides predictive distributions with mean and confidence intervals.
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…
Proposes CAL to learn causal adjacency for better spatiotemporal prediction.
problem Suboptimal performance in spatiotemporal prediction due to out-of-distribution data.
method Causal Adjacency Learning (CAL) method to discover causal relations over graphs.
result Calculated causal adjacency matrix enhances prediction performance on out-of-distribution test data.
New algorithm for efficient prediction intervals in neural networks.
problem Challenges in estimating uncertainty in neural network predictions.
method Applies matrix sketching to approximate Jacobian matrix for efficient uncertainty estimation.
result Produces approximate prediction intervals with competitive performance.
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization, which predicts unobserved entries as linear combinations of latent variables. We g…
The paper tackles entry prediction in row/column-exchangeable matrices with arbitrary missing data.
problem Prediction in matrices with arbitrary missing data.
method Proposes two practical algorithms: one for fast emulation and another for acceleration using algorithmic stability.
result Demonstrates superior performance in synthetic and real-world data sets.
Bayesian NMF model improves predictions and avoids overfitting.
problem Predicting missing values and finding hidden patterns in nonnegative data.
method Flexible and hierarchical prior for Bayesian NMF with Gibbs sampling.
result The proposed model leads to better predictions and avoids overfitting.
Improved bipartite link prediction using 2-hop paths.
problem Link prediction in bipartite networks without node attributes.
method Multiply reconstructed adjacency matrix with symmetrically normalized training adjacency matrix to form 2-hop paths.
result 2-hop paths improve link prediction performance.
Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of rati…
The paper proposes methods for predicting missing values in mixed data matrices.
problem Matrix completion for mixed data types (continuous, binary, ordinal).
method Generalized latent factor models for low-rank matrix estimation with entrywise consistency.
result Tight probabilistic error bounds for the proposed estimators.
Predict missing movie ratings or graph embeddings with low rank matrices.
problem Predicting missing entries in a ratings matrix or graph embeddings with known linear relations.
method Low rank matrix completion approach applied to graph embeddings.
result Effective methods for predicting missing entries in matrices and graph embeddings.
The ubiquitous proliferation of online social networks has led to the widescale emergence of relational graphs expressing unique patterns in link formation and descriptive user node features. Matrix Factorization and Completion have become popular methods for Link Prediction due to the low rank nature of mutual node fr…
Study uses neural networks to predict travel times for public transportation.
problem Inaccurate travel time predictions due to road traffic irregularities.
method Developed two neural network models (MLP and LSTM) using OD travel time matrix.
result Both models can make near-accurate predictions, but LSTM is more susceptible to noise.
Random, but not so much: A parameterization for the returns and correlation matrix of financial time seriesphysics.soc-ph
A parameterization that is a modified version of a previous work is proposed for the returns and correlation matrix of financial time series and its properties are studied. This parameterization allows easy introduction of non-stationarity and it shows several of the characteristics of the true, observed realizations, …
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where and , and allow for arbitrary covariance among the features. For both metho…
The paper addresses ill-conditioning in large spatial data, proposing solutions for prediction and likelihood estimation.
problem Ill-conditioning of the kernel matrix in large spatial data sets.
method Introduction of various optimality criteria and solutions for managing large spatial data.
result Solutions for managing large spatial data, addressing ill-conditioning and improving prediction and likelihood estimation.
Efficient Solution of Portfolio Optimization Problems via Dimension Reduction and Sparsificationq-fin.PM
Efficiently solves large portfolio optimization problems by reducing and sparsifying covariance matrices.
problem Large and dense covariance matrices limit efficient portfolio optimization.
method Dimension reduction and increased sparsity based on machine learning predictions.
result Improved portfolio performance and reduced runtime compared to full dense covariance matrices.
A new method STMF improves missing value prediction using tropical semiring.
problem Limited capability of linear models to model complex relations.
method Sparse Tropical Matrix Factorization (STMF) using tropical semiring.
result STMF outperforms NMF on real data, especially in handling extreme values.
BeMF improves recommendation reliability in recommender systems.
problem Improving reliability in recommender systems beyond accuracy.
method Bernoulli Matrix Factorization (BeMF) for model-based collaborative filtering.
result BeMF selects more reliable predictions, improving recommendation quality.
DeepVir uses deep matrix factorization to predict antivirals for COVID-19.
problem Predicting effective antivirals for COVID-19 using known drug-virus associations.
method Graphical deep matrix factorization with HyPALM optimization.
result DeepVir outperforms state-of-the-art techniques in predicting antivirals for COVID-19.
Hyperparameter tuning via trajectory predictions: Stochastic prox-linear methods in matrix sensingmath.OC
New method predicts and optimizes matrix recovery from noisy measurements.
problem Recovering rank-1 matrices from Gaussian measurements with noise.
method Stochastic prox-linear iterative algorithm with trajectory predictions.
result The method converges linearly with accurate predictions of error.
The data in many disciplines such as social networks, web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this paper, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T+1? If our da…
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired …
New approach to analyze matrix denoising using gradient flow and fixed point equations.
problem Positive semi-definite matrix denoising in extensive-rank and high-dimensional settings.
method Gradient flow and fixed point equations derived from linear pencil techniques of random matrix theory.
result Continuous phase transitions in the extensive-rank and high-dimensional regime.
The paper proposes DEA to make graph neural networks fairer in link prediction.
problem Graph neural networks can unfairly prioritize certain social groups in link prediction.
method Drop Edges and Adapt (DEA) fine-tuning strategy with covariance constraints.
result DEA improves fairness and accuracy in link prediction tasks.
Random matrix theory predicts neural representations generalize well.
problem Understanding why neural representations generalize well in practice.
method Applied random matrix theory to kernel regression and neural networks.
result GCV estimator accurately predicts generalization risk in overparameterized settings.
The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the (unobservable)_denoising_ problem of how to best approximate a low-rank signal matrix bur…
In this paper, we study the effects of different prior and likelihood choices for Bayesian matrix factorisation, focusing on small datasets. These choices can greatly influence the predictive performance of the methods. We identify four groups of approaches: Gaussian-likelihood with real-valued priors, nonnegative prio…
High-dimensional time series prediction is needed in applications as diverse as demand forecasting and climatology. Often, such applications require methods that are both highly scalable, and deal with noisy data in terms of corruptions or missing values. Classical time series methods usually fall short of handling bot…
New model predicts drug effects across various cell types using causal imputation.
problem Predict drug effects across different cell types given limited data.
method Introduces a novel SCM-based model class with latent factor structure and uses Synthetic Interventions estimator.
result Method outperforms other matrix completion approaches in drug repurposing dataset.
Effective Gram matrix predicts deep network generalization.
problem Understanding and predicting deep network generalization.
method Derived a differential equation governing generalization gap, analyzed with effective Gram matrix.
result Effective Gram matrix accurately predicts test loss during training.
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of inference. In this paper, we propose a scalable distributed Bayesian matrix factorizat…
Nonnegative matrix factorization with side information for time series recovery and predictionstat.ML
Motivated by the reconstruction and the prediction of electricity consumption, we extend Nonnegative Matrix Factorization~(NMF) to take into account side information (column or row features). We consider general linear measurement settings, and propose a framework which models non-linear relationships between features …
Enhanced Transformer models predict ETF portfolio performance by optimizing covariance and semi-covariance matrices.
problem Static covariance estimates fail to capture dynamic market fluctuations and non-linear correlations.
method Transformer-based models for real-time covariance and semi-covariance predictions.
result Portfolios optimized with semi-covariance matrix outperform those with standard covariance matrix, especially in volatile conditions.
Collaborative filtering (CF) is a popular technique in today's recommender systems, and matrix approximation-based CF methods have achieved great success in both rating prediction and top-N recommendation tasks. However, real-world user-item rating matrices are typically sparse, incomplete and noisy, which introduce ch…
The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data fitting term and a nuclear norm penalization. Here, we investigate the case where …
Bayes without Underfitting: Fully Correlated Deep Learning Posteriors via Alternating Projectionscs.LG
Bayesian deep learning avoids underfitting by projecting onto null space of generalized Gauss-Newton matrix.
problem Bayesian deep learning often underfits, leading to less accurate predictions than point estimates.
method Proposes a matrix-free algorithm to project onto the null space of the generalized Gauss-Newton matrix, ensuring Bayesian predictions do not underfit.
result The method scales to large models, including vision transformers with 28 million parameters, and avoids underfitting.
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian processes framework, the computational bottlenecks are the inversion of the (regulariz…
Study forecasts volatility and risk in electricity markets using matrix-HAR models.
problem Forecasting volatility and risk in electricity markets.
method Constructed a parsimonious matrix-HAR type model to estimate realized covariation and risk premia in electricity markets.
result Inclusion of longer time horizons and renewable generation information improves forecasts.
Maximizes stock portfolio predictability using machine learning.
problem Improving stock portfolio performance through predictive modeling.
method Optimal constrained weights in the MPP constructed using Elastic Net, Random Forest, and Support Vector Regression models.
result MPP portfolios can outperform or underperform the index based on the time period.
This paper presents novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing en- tries in the general low rank setting. For positive data, we achieve results out- performing the state of the art nuclear norm, both in accuracy and computation…
Short proof shows how ridge regression works with random data.
problem Understanding prediction error in ridge regression with random design.
method Combination of exchangeability arguments, matrix perturbation, and operator convexity.
result Elementary proof of prediction error without complex inequalities.
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong a…
Matrix factorization is at the heart of many machine learning algorithms, for example, dimensionality reduction (e.g. kernel PCA) or recommender systems relying on collaborative filtering. Understanding a singular value decomposition (SVD) of a matrix as a neural network optimization problem enables us to decompose lar…
Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities corresponding to the rows and/or columns of such a matrix. Further information may also…
Matrix SMD converges to unique solution minimizing Bregman divergence.
problem High-dimensional multi-output classification and matrix completion problems.
method Stochastic Mirror Descent with matrix parameters and matrix mirror functions.
result Matrix SMD converges exponentially to the unique solution minimizing Bregman divergence.