This paper analyses the Chinese Sovereign bond yield to find out the principal factors affecting the term structure of interest rate changes. We apply Principal Component Analysis (PCA) on our data consisting of the Chinese Sovereign bond from January 2002 till May 2018 with the different yield to maturity. Then we wil…
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MCPCA analyzes shared factors across multiple data contexts.
problem No tools to recover shared factors across multiple contexts.
method Developed a theoretical and algorithmic framework (MCPCA).
result Reveals shared axes of variation across subsets of contexts.
The paper uses PCA and HMM to forecast stock returns outperforming buy-and-hold.
problem Predicting stock returns accurately.
method Applied PCA to covariance matrix of S&P 500 stocks, used HMM on principal components, and forecasted stock returns.
result The model outperforms buy-and-hold strategy in terms of annualized Sharpe ratio.
Factor Models for Alpha Streamsq-fin.PM
We propose a framework for constructing factor models for alpha streams. Our motivation is threefold. 1) When the number of alphas is large, the sample covariance matrix is singular. 2) Its out-of-sample stability is challenging. 3) Optimization of investment allocation into alpha streams can be tractable for a factor …
Develops a method for causal inference with noisy confounders.
problem Noisy measurements of confounders in treatment effects models.
method Local principal subspace approximation combining K-nearest neighbors matching and PCA.
result Estimators of treatment effects and counterfactual distributions are constructed.
Study non-convex matrix factorization using Riemannian geometry.
problem Matrix completion via non-convex optimization.
method Optimization over a Grassmannian manifold, analyzing principal angles.
result Geodesically convex region in matrix completion cost function.
In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are extracted from least square, principal, iterative principal component, alpha or i…
A new portfolio method using quantum mechanics improves risk diversification.
problem Improving risk-based portfolio construction methods for multi-asset portfolios.
method Schrödinger principal component analysis applied to extract common factors from asset fluctuations.
result The proposed method outperforms conventional risk parity and other risk diversification methods.
Tensor PCA for Factor Modelsecon.EM
Optimal tensor PCA for estimating factors and loadings in high-dimensional panel data.
problem Estimating factors and loadings in high-dimensional panel data with non-negligible correlations.
method Tensor Principal Component Analysis (TPCA) for estimating factors and loadings in a tensor factor model.
result Simple TPCA is optimal for strong factors and can be improved for weak factors with alternating least-squares iterations.
HeMPPCAT improves PCA for data with varying noise.
problem PCA's suboptimal performance on data with heterogeneous noise.
method HeMPPCAT uses a GEM algorithm to estimate factors, means, and noise variances.
result Improved factor estimates and clustering accuracy compared to MPPCA.
Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate covariates, and suggest post-processing transformations to improve interpretability of lat…
Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show…
Paper proposes SDDP for improving time series forecasting with high-dimensional predictors.
problem Improving time series forecasting with high-dimensional predictors.
method SDDP framework that incorporates target variable and lagged observations into factor extraction process.
result SDDP improves predictive accuracy in time series forecasting.
Gradient descent recovers principal components of overparametrized asymmetric matrices without explicit regularization.
problem Asymmetric matrix factorization under overparametrization with minimal rank assumptions.
method Vanilla gradient descent with small random initialization and proper early stopping.
result Gradient descent produces the best low-rank approximation without explicit regularization.
Matrix factorization methods are extensively employed to understand complex data. In this paper, we introduce the cross-product penalized component analysis (XCAN), a sparse matrix factorization based on the optimization of a loss function that allows a trade-off between variance maximization and structural preservatio…
Improved clustering of extra-financial data using NMF with data separation.
problem High correlations and complex data structure in extra-financial datasets.
method Applying non-negative matrix factorization (NMF) with an initial data separation step.
result Enhanced clustering quality compared to PCA.
Generative models converge to data distribution but not principal latent factors.
problem Understanding when generative models converge to the true data distribution.
method Analytical characterisation of transition from memorisation to generalisation in linear generative models.
result Convergence captures matching the bulk of the data distribution but not principal latent factors.
Survey of factor analysis, PCA, variational inference, and VAE.
problem Dimensionality reduction and generative modeling of data.
method Variational inference, factor analysis, probabilistic PCA, and VAE.
result Derivation and explanation of ELBO, EM, and closed-form solutions.
The paper tackles noisy functional data by exploring a multivariate perspective.
problem Noisy functional data measured on discrete points.
method Factor model and principal components analysis.
result The latent signal can be accurately estimated using multivariate methods.
Shrinkage = Factor Modelq-fin.PM
Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternativ…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include flattening the data and applying matrix factorizations such as principal component…
This study analyzes prediction risk for PCR method in latent factor regression models.
problem Prediction risk analysis in latent factor regression models.
method Adaptive PCR method with risk bounds established under factor regression model.
result Unified framework for analyzing various linear prediction methods under factor regression.
AugmentedPCA improves PCA with supervised or adversarial objectives.
problem Lack of reproducible linear analogs for deep latent factor models.
method Augments PCA with supervised or adversarial objectives.
result Improves downstream classification performance and identifies cancer-related genes.
Determining Principal Component Cardinality through the Principle of Minimum Description Lengthcs.LG
PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives…
New method for hyperparameter tuning in sparse matrix factorization.
problem Hyperparameter tuning in sparse matrix factorization.
method Numerical method based on evaluating the zero point of normalization factor in sparse matrix prior.
result Our method outperforms existing algorithms in ground-truth sparse matrix reconstruction.
New FGSPCA method captures grouping and sparse structures in PCA without prior info.
problem Capture grouping and sparse structures in PCA without prior info.
method Truncated regularization with alternating algorithm.
result FGSPCA method reduces model complexity and increases interpretability.
We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting met…
Improved Convergence Speed of Fully Symmetric Learning Rules for Principal Component Analysisstat.ML
Improved convergence speed of principal component analysis through modified learning rules.
problem Slow convergence for covariance matrices with close eigenvalues.
method Introduced an additional term to the objective function to mitigate convergence issues.
result Significantly improved convergence speed confirmed through simulations.
Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works have proposed a probabilistic approach able to infer the number of significant c…
I consider principal Higgs bundles satisfying a notion of numerical flatness (H-nflatness) that was introduced by Bruzzo and Graña Otero. I prove that a principal Higgs bundle is H-nflat is either stable or there exists a Higgs reduction of to a parabolic subgroup of su…
Heterotic Risk Modelsq-fin.PM
We give a complete algorithm and source code for constructing what we refer to as heterotic risk models (for equities), which combine: i) granularity of an industry classification; ii) diagonality of the principal component factor covariance matrix for any sub-cluster of stocks; and iii) dramatic reduction of the facto…
We give a complete algorithm and source code for constructing general multifactor risk models (for equities) via any combination of style factors, principal components (betas) and/or industry factors. For short horizons we employ the Russian-doll risk model construction to obtain a nonsingular factor covariance matrix.…
In this document we are going to derive the equations needed to implement a Variational Bayes i-vector extractor. This can be used to extract longer i-vectors reducing the risk of overfittig or to adapt an i-vector extractor from a database to another with scarce development data. This work is based on Patrick Kenny's …
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin to the singular value decomposition, that maximizes the Bernoulli log-likelihoo…
We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those produced by pre-existing factor analysis approaches. We also establish theoretic…
pPCA speeds up PCA by priming initial estimates for faster, more accurate results.
problem Improving the speed and accuracy of principal component analysis (PCA).
method pPCA is a two-step algorithm: first, an approximate-PCA method primes the data, then exact PCA is applied in the span of the initial estimate.
result pPCA improves accuracy significantly with a small computational cost, outperforming other methods across various datasets.
Algorithm estimates principal eigenvector with adaptive sensing, improving over non-adaptive methods.
problem Estimating principal eigenvector with limited scalar measurements.
method Compressed variant of Oja's algorithm using two adaptive measurements per sample.
result Convergence rate of after iterations, matching information-theoretic lower bound.
Study on liquidity dynamics in Uniswap v3 pools using statistical methods.
problem Characterize liquidity in Uniswap v3 pools.
method Functional principal component analysis (FPCA) and dynamic factor methods.
result Liquidity dynamics in Uniswap v3 pools are well-captured by a low-order Legendre polynomial basis.
A cluster driven log-volatility factor model: a deepening on the source of the volatility clusteringq-fin.ST
We introduce a new factor model for log volatilities that performs dimensionality reduction and considers contributions globally through the market, and locally through cluster structure and their interactions. We do not assume a-priori the number of clusters in the data, instead using the Directed Bubble Hierarchical …
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separation, low rank matrix …
Algorithm learns optimal coordination for strategic agents in uncertain settings.
problem Optimizing rewards for strategic agents with private types and actions.
method Combines delaying mechanism, reward angle estimation, and LinUCB algorithm.
result Near optimal regret bound of for learning optimal policy.
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group,…
This paper uses PCA and FA for feature selection in credit rating.
problem Selecting important features for credit rating prediction.
method Principal Component Analysis and Factor Analysis.
result Factor Analysis reduces feature set significantly without losing much accuracy.
The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR factorization. With the aid of these subspace projections, a fast deflation meth…
In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is stationary to be compatible with principal component analysis. Based on…
Study numerically flat bundles on Fujiki manifolds using algebraic groups.
problem Characterize numerically flat principal bundles on Fujiki manifolds.
method Analyzes holomorphic principal bundles and their quotient structures, proving equivalence of conditions involving numerically flat ad bundles and nef line bundles.
result Establishes equivalence among numerically flat ad bundles, nef line bundles, and degree inequalities for reductions of structure groups.
This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.
problem Identifying pollution sources in rivers for effective environmental management.
method Principal Component Analysis and its modifications, along with Independent Component Analysis and Factor Analysis, are applied to nitrogen pollution source identification.
result PCA and related techniques can be powerful tools for uncovering nitrogen pollution sources in rivers.
HPPCA improves imputation of longitudinal data with missing values.
problem Handling incomplete, high-dimensional longitudinal data with nested sources of variation and temporal dependency.
method Hierarchical probabilistic principal component analysis (HPPCA) with a two-level latent factor model and Gaussian process.
result HPPCA outperforms standard PPCA and multivariate functional PCA in imputation accuracy, even under heavy missingness and model misspecification.