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.
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.
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.
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 algorithm speeds up fair clustering by 12x.
problem Achieving fair clustering in scalable algorithms.
method s-FairSC algorithm incorporating nullspace projection and Hotelling's deflation.
result s-FairSC is 12x faster and maintains fairness.
One of the first things to do while planning a trip is to book a good place to stay. Booking a hotel online can be an overwhelming task with thousands of hotels to choose from, for every destination. Motivated by the importance of these situations, we decided to work on the task of recommending hotels to users. We used…
Hotel2vec learns hotel embeddings from multiple data sources.
problem Cold-start problem for hotels with insufficient click data.
method Self-supervised neural network architecture combining user clicks, hotel attributes, and geographic info.
result Improved downstream task predictions with structured hotel attributes.
Recognizing a hotel from an image of a hotel room is important for human trafficking investigations. Images directly link victims to places and can help verify where victims have been trafficked, and where their traffickers might move them or others in the future. Recognizing the hotel from images is challenging becaus…
PriceAggregator optimizes hotel price fetching to increase Agoda's bookings.
problem Limited QPS from suppliers causes many user searches to be ignored.
method Intelligently determines queries to suppliers for price fetching.
result PriceAggregator increases Agoda's bookings significantly.
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 present a real-world conversational AI system to search for and book hotels through text messaging. Our architecture consists of a frame-based dialogue management system, which calls machine learning models for intent classification, named entity recognition, and information retrieval subtasks. Our ch…
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 study examines how market completeness is lost when filtering down the information set.
problem Loss of market completeness under filtration shrinkage.
method Bayesian filtering approach to analyze local martingale deflators and their projections.
result Projections of deflators in smaller filtrations are not sufficient to span all local martingale deflators.
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.
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…
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.
New methods explain NE embeddings by identifying key variables.
problem Lack of interpretability in NE techniques.
method Combining PCA, Q-residuals, Hotelling's T2, and visualization.
result Identifies discriminatory features not seen in standard approaches.
Study suggests variable selection may not significantly reduce power in multivariate tests.
problem The feasibility of parsimonious variable selection in Hotelling's T2-test.
method Investigation of power loss when selecting small subsets of variables from multivariate data.
result Some evidence suggests no significant power loss over a wide range of alternatives.
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…
Proposes RTL model for sentiment classification and key word detection in online reviews.
problem Sentiment classification and key word detection in online reviews for hospitality industry.
method Regularized Text Logistic (RTL) regression model.
result RTL model achieves satisfactory classification performance and identifies key word features.
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 fast method for sparse PCA reduces computation time.
problem Time-consuming implementation of SPCA on high-dimensional data.
method Subspace projections using Household QR factorization for efficient deflation.
result Developed SPCA-SP method maintains good tradeoffs between various criteria.
Researchers solved a model of an exhaustible resource with stochastic discoveries.
problem Optimal exploration of an exhaustible resource with uncertain discoveries.
method Impulse control and Poisson process of new discoveries.
result A frontier of critical levels of proven reserves exists, above which exploration is stopped.
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.
H. Hotelling proved that in the n-dimensional Euclidean or spherical space, the volume of a tube of small radius about a curve depends only on the length of the curve and the radius. A. Gray and L. Vanhecke extended Hotelling's theorem to rank one symmetric spaces computing the volumes of the tubes explicitly in these …
Many-to-one RNN predicts user hotel clicks from browsing history.
problem Predicting user hotel clicks from browsing history.
method Combines rule-based algorithm with Gated RNN to sort accommodations.
result Promising results but computationally demanding.
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.
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.
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 …
The growth of the modern knowledge-based economy is becoming less and less dependent on tangible assets and more on intangible ones. In this context, the role of human capital in the value creation process has become central. Despite the large amount of scientific work on human capital phenomena, little research has re…
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.
Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a sparse canonical correlation analysis by adding l1 constraints on the canonical vec…
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…
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).