Identifies patient-specific root causes of disease using structural equation models.
problem Detecting significant variables in complex diseases that differ between patients.
method Defining patient-specific root causes as exogenous errors in a structural equation model, quantifying predictivity using Shapley values, and developing a fast algorithm called Root Causal Inference.
result Significant improvements in accuracy by uncovering root causes with large effect sizes at the individual level but clinically insignificant effect sizes at the group level.
New method identifies root causes in presence of latent confounding.
problem Identifying root causes in the presence of latent variables.
method Extract Errors with Latents (EEL) procedure for inferring root causes.
result Superior accuracy and robustness compared to previous methods.
Bayesian networks with latent variables are characterized and their likelihoods compared.
problem Characterizing and comparing likelihoods of Bayesian networks with latent variables.
method Characterized likelihood function and empirical Bayesian network. Proved dominance of global maximum likelihood from empirical model.
result The global maximum likelihood of the original Bayesian network is attained if and only if parameters are consistent with empirical model.
New definition of patient-specific root causes of disease using counterfactuals.
problem Lack of rigorous mathematical formulation for automatic detection of root causes.
method Proposes a counterfactual definition matching clinical intuition and uses Shapley values for causal contribution scores.
result Adapts to disease prevalence, accounts for noisy labels, and admits fast computation.
New method identifies causal order without sparsity assumptions.
problem Causal order discovery in observational data.
method Sequential procedure to directly identify causal order.
result Direct identification of causal order without sparsity assumptions.
Paper tackles anomaly detection and RCA in dynamical systems using ICODE Networks.
problem Anomalies in dynamical systems impact performance and reliability.
method Proposes ICODE Networks for anomaly detection, RCA, and type classification.
result Demonstrates the ability to accurately detect anomalies, classify types, and pinpoint origins.
We describe a formal approach to identify 'root causes' of outliers observed in n variables X1,…,Xn in a scenario where the causal relation between the variables is a known directed acyclic graph (DAG). To this end, we first introduce a systematic way to define outlier scores. Further, we introduce the concep…
CD-RCA method identifies causal relationships in prediction errors without predefined graphs.
problem Challenges in diagnosing prediction errors due to lack of transparency in black-box models.
method Causal-Discovery-based Root-Cause Analysis (CD-RCA) method that estimates causal relationships without predefined causal graphs.
result CD-RCA outperforms heuristic attribution methods in identifying variable contributions to prediction errors.
The paper proposes a new probability distribution for rooted trees.
problem Overfitting in tree selection for statistical models.
method Bayesian approach with a generalized probability distribution for rooted trees.
result Recursive methods to evaluate the probability distribution without approximations.
Geometric models for Lie algebras from simple singularities.
problem Classifying simply-laced simple Lie algebras.
method Using polygonal wheels derived from Milnor fibers of simple singularities.
result Geometric root systems are isomorphic to Lie algebras.
A new probability distribution on full rooted trees helps in model selection.
problem Model selection for full rooted trees is problematic due to their hierarchical structure.
method Assume a prior distribution on full rooted trees, using Bayes decision theory.
result The proposed distribution enables optimal model selection and prevents overfitting.
Optimizes AMM markets with a new framework reducing complex optimization to simpler root finding.
problem Optimizing routing and arbitrage in AMM markets.
method Restricts search to boundary of optimal space using marginal prices, reducing high-dimensional optimization to lower-dimensional root finding.
result Significantly faster and more robust performance compared to the original convex optimization method.
We present a novel k-way high-dimensional graphical model called the Generalized Root Model (GRM) that explicitly models dependencies between variable sets of size k > 2---where k = 2 is the standard pairwise graphical model. This model is based on taking the k-th root of the original sufficient statistics of any univa…
Lasso is a seminal contribution to high-dimensional statistics, but it hinges on a tuning parameter that is difficult to calibrate in practice. A partial remedy for this problem is Square-Root Lasso, because it inherently calibrates to the noise variance. However, Square-Root Lasso still requires the calibration of a t…
Turbiner's conjecture posits that a Lie-algebraic Hamiltonian operator whose domain is a subset of the Euclidean plane admits a separation of variables. A proof of this conjecture is given in those cases where the generating Lie-algebra acts imprimitively. The general form of the conjecture is false. A counter-example …
Bounds on knot polynomials for Lie superalgebras of type I.
problem Determining genus bounds for knot polynomials colored by Lie superalgebra representations.
method Proved bounds on the t-degree of knot polynomials, relating it to the number of odd roots and the genus of the knot. result Proved bounds on knot polynomials for Lie superalgebras of type I, showing equality for certain knots.
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to …
We show that the A2 clasps in the Karoubi envelope of A2 spider satisfy the recursive formula of the two-variable Chebyshev polynomials of the second kind associated with a root system of type A2. The A2 spider is a diagrammatic description of the representation category for Uq(sl3) and the $…
New method improves simulation efficiency in high dimensions.
problem Efficiency in estimating functionals of conditional expectations in high dimensions.
method Kernel ridge regression exploiting smoothness of conditional expectation.
result Effective reduction of the curse of dimensionality, bridging convergence rates.
Paper tackles anomaly detection with missing causal knowledge.
problem Detect anomalies with missing structural knowledge.
method Simple, efficient methods for polytree causal graphs.
result Heuristic identifies root causes based on anomaly scores.
Visualizes futures markets using particle physics tools.
problem Understanding high-velocity data in futures markets.
method Uses ROOT, an open-source data-analysis tool, to reconstruct and visualize message-based data.
result Allows stakeholders to gain a better understanding of markets and monitor effectively.
Paper proposes CIV estimator for categorical instruments in small sample settings.
problem Estimation with categorical instruments in settings with few observations per category.
method CIV estimator leveraging regularization assumption for latent categorical variable.
result CIV estimator is asymptotically normal, efficient, and semiparametrically efficient under homoskedasticity.
Identifies shifts in causal mechanisms between related datasets using ANMs.
problem Estimating the full causal structure from data is challenging; focus on identifying shifts in causal mechanisms.
method Assumes nonlinear additive noise models, uses Jacobian of score function for mixture distribution to identify shifts.
result Shows applicability of the approach on synthetic and real-world data.
In this paper are given explicit calculations of Laplace operator spectrum for smooth real/complex-valued functions on all connected compact simple rank four Lie groups with biinvariant Riemannian metric, corresponding to root systems B4, C4, D4 and established a connection of obtained formulas with the number…
We generalize the Toda lattice hierarchy by considering N+M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are ε-series of differential polynomials in the dependent variables, and we use them to provide a Lax pair definition of th…
We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed MA coefficients the likelihood function is optimized in the autoregressive variables Φ's by a closed form formula generalizing regression c…
We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl representations of the braid group. We use these to provide new quantum algorithms for appro…
Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detection and root finding procedure to learn the high dimensional sparse generalized linear models and denote this method by GSDAR. Based on the …
iKF method uncovers complex variable interactions for scientific discovery.
problem Limited interpretability of existing models in decision-making applications.
method Iterative Kings' Forests (iKF) method to uncover multi-order interactions.
result iKF provides strong interpretive power for explainable modeling.
A linear and lagged relationship between inflation and labor force change rate, p(t)= A1dLF(t-t1)/LF(t-t1)+A2 was found for developed economies. For the USA, A1=4.0, A2=-0.03075, and t1=2 years. It provides a RMS forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best amon…
Two-root Riemannian manifolds have no odd-dimensional examples.
problem Characterizing Riemannian manifolds with specific eigenvalues of the Jacobi operator.
method Investigation of k-root manifolds, focusing on one-root and two-root cases. result There are no two-root Riemannian manifolds of odd dimension.
In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a generalized m-th root metric is conformal to a m-th root metric, then both of them redu…
Uniqueness of quasi-roots explored in right-angled Artin groups.
problem Uniqueness of quasi-roots in right-angled Artin groups.
method Introducing quasi-roots and studying their uniqueness.
result Uniqueness of quasi-roots established in right-angled Artin groups.
We discover a new example of a generic rank 2-distribution on a 5-manifold with a 6-dimensional transitive symmetry algebra, which is not present in Cartan's classical five variables paper. It corresponds to the Monge equation z' = y + (y'')^(1/3) with invariant quartic having root type [4], and a 6-dimensional non-sol…
Study differential properties of matrix square roots in specific cases.
problem Understanding matrix square roots in semi-simple, symmetric, and orthogonal cases.
method Analysis of differential and metric structures of real square roots of matrices under specific conditions.
result Differential properties of matrix square roots in semi-simple, symmetric, and orthogonal cases.
Identifies root causes of outliers in unknown cyclic graphs.
problem Outliers in unknown cyclic graphs with linear structural equations.
method Identifies a short list of potential root causes based on strong perturbation and structural equations.
result The shortlist includes true root causes and their parents on the cycle.
D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary number-theoretic conditions that describe the values of n for which an nth root exis…
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
CROC identifies the earliest-changing stream as the root cause in multi-stream data.
problem Distribution-free root cause analysis in multi-stream data with unknown distributional changes.
method Conformal p-values and finite-sample valid confidence sets.
result CROC efficiently isolates the root cause under minimal assumptions.
From analysis of a big variety of different knots we conclude that at q which is an root of unity, q^{2m}=1, HOMFLY polynomials in symmetric representations [r] satisfy recursion identity: H_{r+m} = H_r H_m for any A, which is a generalization of the property H_r = (H_1)^r for special polynomials at q=1. We conjecture …
Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable surface N_g of genus g. We explore the existence of roots and, following the work of …
New model identifies patient-specific disease root causes.
problem Identifying root causes of complex diseases varying between patients.
method Generalized Root Causal Inference (GRCI) algorithm for heteroscedastic noise model.
result GRCI accurately extracts patient-specific root causes.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.
problem Improving statistical efficiency in stochastic optimization.
method Integrates a diminishing stepsize strategy into ROOT-SGD.
result Achieves optimal convergence rates with improved stability and precision.
The study of random positive 3-strand braids reveals patterns in the roots of their Alexander polynomials.
problem Investigating the roots of Alexander polynomials of random positive 3-strand braids.
method Experimental data analysis, conjectures refinement, and proof of results using tools like the signature function of links and Lyapunov exponent of the Burau representation.
result Generically, at least 69% of the roots of Alexander polynomials are on the unit circle, with a large root-free region near the origin.
In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal β-change of an m-th…
Unified quantum invariants via intersections of embedded Lagrangians.
problem Unified quantum invariants for Uq(sl(2)). method State sum of Lagrangian intersections in configuration spaces.
result Recovery of coloured Jones and Alexander polynomials.
Study proposes a new method for better price prediction using machine learning and metaheuristics.
problem Challenges in predicting prices due to correlated variables and computational efficiency.
method Introduces a novel decision fusion approach combining Elastic Net and MOPSO for variable selection and prediction.
result The proposed method outperforms traditional approaches in terms of accuracy and efficiency.