A new method to explain black box models using Shapley values.
problem Quantifying the impact of individual input variables in black box functions.
method Cohort Shapley measure based on cooperative game theory, using similarity cohorts.
result Introduces a new squared cohort Shapley value for variable importance.
This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To co…
Paper proposes a uniqueness Shapley measure to compare variable importance.
problem Comparing the importance of different variables in identifying subjects.
method Uses Shapley value to combine reductions in log cardinality due to revealing variables.
result Demonstrates speedup in calculating variable importance.
Study optimal trading strategies with differing views and market prices.
problem Maximizing portfolio value with subjective asset value vs market price.
method Mean-field game approach to analyze interactions among agents with differing signals.
result Cross-sectional distribution of agents' inventories and price distribution dependence on shared information.
Solves the equity premium puzzle without calibrated values.
problem Equity premium puzzle in finance.
method Derived new model from 4 different equations, found subjective time discount factor and coefficient of relative risk aversion.
result Calculated values and risk attitude determination align with empirical literature.
Pairwise ranking aligns subjective clinical evaluations with objective indicators.
problem Aligning subjective clinical evaluations with objective indicators for improved diagnosis.
method Pairwise ranking methods to align subjective evaluations with objective indicators.
result The resulting score improves classification accuracy and provides a nuanced severity assessment.
Demonstrates ABCE's fairness analysis in complex systems.
problem Complex stochastic systems and subjective value criteria.
method Agent-based computational economics.
result Shows ABCE's capability for fairness analysis.
Paper introduces ρ-Perfect to estimate model-human correlation in subjective datasets.
problem Inherent noise in subjective ratings limits model-human correlation quantification.
method Defines ρ-Perfect as highest achievable correlation between perfect predictor and human ratings. Estimates based on heteroscedastic noise scenarios. result Demonstrates ρ-Perfect can distinguish model limitations from data quality issues. The study proposes algorithms to minimize rating discordance in missing data.
problem Missing ratings in combined rating lists.
method Optimization models and algorithms that minimize total rating discordance.
result The proposed methods outperform state-of-the-art imputation methods in accuracy.
Solves equity premium puzzle with time-varying variables.
problem Equity premium puzzle.
method Consumption Capital Asset Pricing Model with time-varying subjective time discount factors.
result Calculated coefficient of relative risk aversion (CRRA) is around 4.40.
New model solves equity premium puzzle with risk aversion coefficient.
problem Equity premium puzzle in financial markets.
method Developed a new model incorporating investor risk behavior, tested with specific coefficients.
result Validated model with empirical studies, confirming coefficient of 1.033526.
Unified method for discovering biclusters and triclusters in longitudinal data.
problem High-dimensional, sparsely sampled, irregularly observed longitudinal data.
method Tri-SfSVD, a unified sparse functional Singular Value Decomposition framework.
result Identified localized structures at the subject, subject-feature, and subject-feature-time levels.
The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the approach presented is based on a hypothetical transfer of the original li…
New theory tackles AGI by breaking data constraints and minimizing global risk.
problem Current AI's limitations in handling complex real-world data and making reasonable judgments.
method Developed subjectivity learning theory to break data constraints and minimize global risk.
result Subjectivity learning holds a lower risk bound than traditional machine learning.
Geometry-aware models improve cross-subject EEG decoding accuracy.
problem Strong inter-subject variability in motor imagery decoding.
method Discriminative Congruence Transform (DCT), Deep Linear DCT (DLDCT), Deep DCT-UNet (DDCT-UNet).
result Improves transductive cross-subject accuracy by 2-3%.
This paper proposes Deep Hyperalignment (DHA) as a regularized, deep extension, scalable Hyperalignment (HA) method, which is well-suited for applying functional alignment to fMRI datasets with nonlinearity, high-dimensionality (broad ROI), and a large number of subjects. Unlink previous methods, DHA is not limited by …
Develops a hierarchical model for analyzing longitudinal data on manifolds.
problem Correlation between intra-subject measurements in nonlinear manifolds.
method Geodesic hierarchical models extended to Bézier spline trends.
result Validated on osteoarthritis data, improving disease progression classification.
We develop a general method of proving the ellipticity of boundary value problems for the stationary vacuum space time, by showing that the stationary vacuum field equations are elliptic subjected to a geometrically natural collection of boundary conditions in the projection formalism. Using this we prove the manifold …
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjec…
In the previous work ([14]) we introduced the well-posed boundary conditions P−,L0 and P+,L1 for the odd signature operator to define the refined analytic torsion on a compact manifold with boundary. In this paper we discuss the gluing formula of the refined…
In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…
We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online video-game (http://arora.ccs.neu.edu) where players are challenged to distinguish actual financial market returns from random temporal permut…
We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called {\it probability of drawdown}, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its maximum value to date. We assume that the portfolio is subject to a payout that…
Develops a method for extracting sources in multi-subject fMRI data.
problem Analyzing brain imaging datasets from multiple subjects with varying levels of jointness.
method Deflation-based algorithm using higher order cumulants and thin-SVD factorization.
result The algorithm accurately identifies joint, partially-joint, and individual sources with high precision.
The future value of a security is described as a random variable. Distribution of this random variable is the formal image of risk uncertainty. On the other side, any present value is defined as a value equivalent to the given future value. This equivalence relationship is a subjective. Thus follows, that present value…
New method considers subjectivity in text analysis using 'Room Theory'.
problem Detecting emotions in text considering subjective context.
method Framework Theory, Word2Vec, similarity measure between words.
result Measures relative relevance of emotions for a document.
Paper extends Bayes Theorem for interval probability estimates.
problem Real-world input probabilities are often interval estimates, not precise.
method Developed IT2 version of Bayes Theorem and a novel algorithm for encoding intervals.
result Conservative method avoids invalid output results from inconsistent input.
A new PLL method uses class activation values to improve robustness.
problem Weakly supervised learning with noisy data and adversarial perturbations.
method Subjective logic with class activation values for uncertainty representation and label weight re-distribution.
result More robust predictions under high noise levels, out-of-distribution examples, and adversarial perturbations.
Study on spectral asymptotics in elasticity on smooth manifolds.
problem Analyzing spectral asymptotics in linear elasticity on smooth manifolds.
method Established two-term spectral asymptotics for boundary value problems in linear elasticity.
result Corrected erroneous results in previous studies.
Improved fMRI activation detection for single-subject studies.
problem Challenges in detecting activation in low-signal fMRI studies.
method Model-based approach using MixfMRI R package.
result Reliable activation detection in single-subject fMRI studies.
We consider the classical optimal dividends problem under the Cramér-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value functi…
Deriving insights from high-dimensional data is one of the core problems in data mining. The difficulty mainly stems from the fact that there are exponentially many variable combinations to potentially consider, and there are infinitely many if we consider weighted combinations, even for linear combinations. Hence, an …
No arbitrage holds if a Pareto solution exists for vector-valued utility maximization.
problem Existence of no arbitrage in markets with transaction costs and multiple assets.
method Prove no arbitrage condition equivalent to Pareto solution for vector-valued utility maximization.
result A consistent price process can be constructed from the Pareto maximizer.
We extend the Vasiček loan portfolio model to a setting where liabilities fluctuate randomly and asset values may be subject to systemic jump risk. We derive the probability distribution of the percentage loss of a uniform portfolio and analyze its properties. We find that the impact of liability risk is ambiguous and …
Digital currencies and cryptocurrencies have hesitantly started to penetrate the investors, and the next step will be the regulatory risk management framework. We examine the Value-at-Risk and Expected Shortfall properties for the major digital currencies, Bitcoin, Ethereum, Litecoin, and Ripple. The methodology used i…
We study the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we show that the renormalized volume is continuous under the appropriate notion of limit. This result generalizes previous work in the subject…
Study vector-valued robust control under uncertainty.
problem Dynamic stochastic control with multi-objective criteria under model uncertainty.
method Robust minimax approach, set-valued framework, dynamic programming principle.
result Derived weak and strong versions of dynamic programming principle for vector-valued control problems.
Derives an approximation algorithm for continuous submodular maximization without derivative information.
problem Maximizing a continuous submodular function with only function values and no derivative information.
method Black-box Continuous Greedy algorithm for DR-submodular functions, extended to stochastic setting.
result Achieves a (1−1/e)OPT−ε approximation guarantee with O(d/ε3) function evaluations. LRF framework predicts and interprets longitudinal response trajectories.
problem Sparse and irregular data in longitudinal studies.
method Longitudinal Random Forest (LRF) framework with adaptive node-wise trajectory estimation.
result LRF outperforms competing methods in predicting and interpreting longitudinal trajectories.
Study optimizes insurance liability cash flows with regulatory capital requirements.
problem Valuation of insurance liabilities under regulatory capital constraints.
method Multiple-prior optimal stopping theory applied to insurance liabilities, considering hypothetical transfer and repeated capital requirements.
result Proposes a valuation functional for non-replicable cash flows, incorporating a margin for regulatory capital considerations.
Investor optimizes portfolio to manage risk with heavy-tailed stock returns.
problem Managing risk in portfolios with heavy-tailed stock returns.
method Markov Decision Process and dynamic programming for optimal strategies and value function.
result Optimal strategies and value function maximizing expected utility for both parametric and non-parametric distributions.
Fluctuations in heart rate are intimately tied to changes in the physiological state of the organism. We examine and exploit this relationship by classifying a human subject's wake/sleep status using his instantaneous heart rate (IHR) series. We use a convolutional neural network (CNN) to build features from the IHR se…
Proposes a VAE variant for ordinal content factors.
problem Isolating ordinal-valued content factors in deep latent variable models.
method Introduces a partially ordered set (poset) structure and a conditional Gaussian spacing prior model.
result Significant improvements in content-style separation over previous non-ordinal approaches.
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
Develops a framework for optimal investment in assets with different liquidity constraints.
problem Optimal investment-consumption problem for a utility-maximizing investor with lower-bound constraints.
method Generalized martingale approach and decomposition of the problem into subproblems.
result Explicit formulas for optimal strategies derived for power-utility functions.
New decision support systems use prediction sets to help experts update their predictions, improving performance.
problem Challenges in explaining and updating predictions from decision support systems.
method Developed a methodology leveraging nested structure of prediction sets and counterfactual monotonicity to improve performance.
result Limiting experts' agency leads to better performance in decision support systems based on prediction sets.
A new framework for robust risk measurement and portfolio optimization.
problem Uncertainty in mean-covariance space and portfolio optimization challenges.
method Modeling uncertainty with Gelbrich distance and prior structural information, related to optimal transport theory.
result Mean-covariance robust portfolio optimization simplifies to Markowitz model with a regularization term.
A new method for efficient inference in sequential latent-variable models.
problem Computational challenges in integrating subject-specific random effects.
method Anchored variational inference framework to approximate posterior distributions.
result The method achieves accurate estimation with significant computational gains.