New method clusters tensors with heteroskedastic noise.
problem Clustering tensors with varying noise levels.
method Two-stage method: subspace estimation followed by approximate k-means. result Proves exact clustering for SNR above computational limit.
New algorithm improves heteroskedastic PCA performance.
problem Estimating low-rank matrix subspace from noisy data.
method Deflated-HeteroPCA algorithm, dividing spectrum into subblocks.
result Near-optimal and condition-number-free statistical guarantees.
Paper investigates existence of deflators in financial markets.
problem Existence of equivalent local martingale deflators in semimartingale markets.
method Characterization of deflators using modified semimartingale characteristics.
result Existence of deflators can be characterized by modified semimartingale characteristics.
In this paper, we implement a stochastic deflator with five economic and financial risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero-coupon bonds, vanilla options, and corporate cou…
We solve optimal consumption in a market with bounded risk.
problem Optimal consumption in a semimartingale market with bounded risk.
method Use supermartingale deflators to prove strong duality.
result Strong duality and complete characterisation of optimal consumption.
The paper analyzes deflation for estimating a low-rank spike in large tensors with noise.
problem Estimating a low-rank symmetric spike in large tensors with additive Gaussian noise.
method Characterization of deflation performance in terms of vector alignments and weights.
result Understanding deflation mechanism in noisy conditions and designing more efficient methods.
Paper develops methods for PCA inference with missing data and heteroskedastic noise.
problem Constructing confidence regions for PCA in high dimensions with missing data and heteroskedastic noise.
method Proposes HeteroPCA and develops non-asymptotic distributional guarantees for valid inference.
result Valid inference on principal subspace and spiked covariance matrix with missing data.
We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller informatio…
Study resolves duality gap in optimal consumption with random income termination.
problem Optimal consumption in a market with randomly terminating income.
method Established rigorous duality theory using supermartingale deflators.
result Closed duality gap and characterized optimal wealth process.
Paper optimizes tensor deflation for non-orthogonal signals.
problem Recovering low-rank signals from noisy tensors with correlated components.
method Developed an asymptotic analysis and optimized deflation procedure using random tensor theory.
result Proposed an efficient tensor deflation algorithm that optimizes a parameter introduced in the deflation mechanism.
This paper analyzes how errors accumulate in PCA's deflation method.
problem Error accumulation in PCA's deflation method.
method Mathematical analysis of inexact Hotelling's deflation method in two scenarios.
result Characterization of error propagation in PCA's deflation method.
Let F⊂G be two filtrations and S be a F semimartingale possessing a F local martingale deflator. Consider τ a G stopping time. We study the problem whether Sτ− or Sτ can have G local martingale deflators. A suitable theoretical framework…
The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.
problem Understanding the training dynamics of gradient flow on tensor decomposition.
method Empirical observation and mathematical proof of gradient flow dynamics for orthogonally decomposable tensors.
result Gradient flow dynamics for orthogonally decomposable tensors follows a tensor deflation process, recovering all tensor components.
We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal components simultaneously using manifold optimization techniques to enforce orth…
Study analyzes Hotelling-type tensor deflation for spiked tensors, providing insights into signal and noise.
problem Characterizing singular values and alignments in Hotelling-type tensor deflation.
method Asymptotic study of Hotelling-type tensor deflation in large dimensional regime using random tensor theory.
result Characterization of singular values and alignments at each step of the deflation procedure.
The paper studies optimal maps between hyperbolic surfaces, focusing on their rigidity and obstructions.
problem Finding optimal Lipschitz maps between hyperbolic surfaces and understanding their rigidity and obstructions.
method Introducing deflations, optimal maps to trees that obstruct optimal maps between surfaces, and using a smooth orthogeodesic foliation.
result Deflations are the main obstructions to optimal maps between hyperbolic surfaces, and they are essentially the only ones.
DFSOS improves sparse discriminant analysis for high-dimensional data.
problem Sparse discriminant analysis in high-dimensional settings with feature selection.
method Deflation-Free Sparse Optimal Scoring (DFSOS) using Bregman iteration and orthogonality-constrained optimization.
result DFSOS achieves comparable or better classification accuracy than deflation-based methods.
Study arbitrage theory without numéraire, generalizing NUPBR.
problem Arbitrage theory in markets without numéraire.
method Disintegration of probability space into crash times.
result Generalization of NUPBR to no unbounded profits with bounded risk.
Study analyzes accuracy of tensor deflation in noisy conditions.
problem Analyzing accuracy of tensor deflation in noisy conditions.
method Asymptotic study of Hotelling-type tensor deflation in large tensor dimensions.
result Characterization of estimated singular values and singular vector alignments.
New analysis improves black-box k-PCA algorithms, reducing parameter loss.
problem Designing efficient k-PCA algorithms with black-box access to a 1-PCA oracle. method Black-box deflation methods, analyzing ePCA and cPCA approximations.
result Deflation methods suffer no asymptotic parameter loss for k-cPCA in feasible regimes. We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integ…
Paper proposes a new deflation varimax method for vintage factor analysis.
problem Finding a scientifically meaningful low-dimensional representation of data.
method Deflation varimax procedure for orthogonal matrix rotation.
result The proposed method achieves minimax optimal factor loading estimation.
No arbitrage in financial markets with special semimartingales.
problem Proving the absence of arbitrage in non-numéraire financial markets.
method Proving the absence of arbitrage using a multiplicative special semimartingale deflator.
result The market is free of arbitrage if and only if there exists a multiplicative special semimartingale deflator.
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is com…
New method deflates manifolds to visualize high-dimensional data.
problem Failure of nonlinear dimensionality reduction methods on simple manifolds.
method Iterative deflation of differential operators using single-coordinate estimates.
result Empirically, recovers novel embeddings on real-world and synthetic datasets.
A new method for sparse PCA using orthogonal rotations and soft-thresholding.
problem Sparse PCA with a new basis using orthogonal rotations.
method Initialize with leading principal components, apply kimesk orthogonal rotation, and soft-threshold the rotated components. result The proposed method is more stable and explains more variance compared to alternatives.
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…
Unified framework models multiple financial and insurance term structures.
problem Modeling multiple term structures in various markets.
method Extended Heath-Jarrow-Morton (HJM) approach under real-world probability.
result Characterization of local martingale deflators and existence of affine realizations.
Bayesian method improves dictionary learning for complex problems.
problem Efficiently identifying relevant dictionary entries for complex inverse problems.
method Bayesian group sparsity coding and deflation steps to compress and identify relevant subdictionaries.
result Significant computational complexity reduction and improved glitch detection in LIGO experiment.
The paper provides a new uniform tail bound for empirical processes.
problem Developing a uniform tail bound for empirical processes indexed by a class of functions.
method Introducing a deflation step to the standard generic chaining argument, and using a natural seminorm based on Cramér functions.
result Established a new uniform tail bound for empirical processes.
A new method inflates and deflates data manifolds to estimate densities without losing universality.
problem Density estimation on low-dimensional manifolds with non-Euclidean support.
method Inflation-deflation approach using Normalizing Flows with added noise.
result Exact estimation of densities on manifolds with sufficient conditions and Gaussian noise approximation.
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with …
Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.
problem Maximizing lifetime utility from wealth over an infinite horizon.
method Develops a duality theory using deflators and supermartingale properties, extending previous work.
result Establishes a strong duality theorem for infinite horizon utility maximization under minimal no-arbitrage assumptions.
I sketch a program for a microeconomic theory of the main component of the business cycle as a recurring disequilibrium, driven by incompleteness of the financial market and by information asymmetries between borrowers and lenders. This proposal seeks to incorporate five distinct but connected processes that have been …
A constrained informationally efficient market is defined to be one whose price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which despite its simplicity, generates new insights. In particular, it is show…
Develops a method to estimate the shadow riskless rate from empirical data.
problem No risky asset in market, need for a shadow riskless rate.
method PCA, SVD, regularization to estimate SRR from correlated geometric Brownian motion.
result Estimates the shadow riskless rate from empirical datasets.
KLD token adjusts supply based on macroeconomic debt index, creating deflationary effect.
problem Managing deflationary pressures in digital assets.
method Debt-indexed supply adjustments linked to macroeconomic data.
result Deflationary mechanism strengthens as debt rises.
We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).
This paper considers an initial market model, specified by its underlying assets S and its flow of information F, and an arbitrary random time τ which might not be an F-stopping time. As the death time and the default time (that τ might represent) can be seen when they occur only, the progress…
Singapore's cooling measures did not increase housing wealth overall.
problem The impact of cooling measures on housing wealth distribution.
method Examined Singapore's cooling measures over ten rounds, analyzing welfare from housing wealth.
result Welfare from housing wealth in the last round might not be higher than before 2009, depending on the deflator.
There is an extensive historical dataset on real GDP per capita prepared by Angus Maddison. This dataset covers the period since 1870 with continuous annual estimates in developed countries. All time series for individual economies have a clear structural break between 1940 and 1950. The behavior before 1940 and after …
In a semimartingale financial market model, it is shown that there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes.
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009].
Sharp rates found for learning with dependent data, avoiding sample size deflation.
problem Learning with dependent data and square loss.
method Combining weak sub-Gaussian class and mixed tail generic chaining.
result Achieves a rate that only depends on class complexity and second order statistics.
New method finds linear relationships across multiple data blocks using proximal gradient descent with ℓ1 constraint.
problem Finding leading generalized eigenvectors for multi-block CCA.
method Proximal gradient descent with ℓ1 constraint. result Rate-optimal solution under suitable assumptions.
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can be computed one by one, repeatedly solving the single-component problem and def…
The paper describes how martingales can be represented after a random time in financial models.
problem Representing martingales after a random event in financial markets.
method Explicit representation of G-local martingales in terms of F-local martingales and parameters of the random time.
result Comprehensive representation of G-local martingales, complementing previous work.
The aim of this paper is to compare statistical properties of a bubble period with those of the anti-bubble period in stock markets. We investigate the statistical properties of daily data for the Nikkei 225 index in the 28-year period from January 1975 to April 2003, corresponded to the periods of bubbles and anti-bub…