A new method for non-rigid point set registration reduces computational complexity.
problem Efficiently registering non-rigid point sets with large numbers of points.
method Structured Analytic Coherent Point Drift (Analytic-CPD) reformulates CPD for structured analytic mappings.
result Analytic-CPD reduces computational complexity by controlling the deformation model's dimensionality.
Paper estimates upper bound of analytic torsion under Arakelov metric.
problem Estimating the analytic torsion under Arakelov metric.
method Defined and analyzed the regularized determinant of Laplacian, providing an asymptotic upper bound.
result The logarithm of analytic torsion is asymptotically upper bounded by g for g>1. We discuss the problem of risk estimation in the classification problem, with specific focus on finding distributions that maximize the confidence intervals of risk estimation. We derived simple analytic approximations for the maximum bias of empirical risk for histogram classifier. We carry out a detailed study on usi…
New Hessian estimators for Riemannian manifolds with reduced bias.
problem Estimating Hessians on Riemannian manifolds with reduced bias and computational efficiency.
method Introducing new stochastic zeroth-order Hessian estimators using O(1) function evaluations. result Achieved a bias bound of order O(γδ2) for analytic real-valued functions. Proposes a method to estimate neural network statistics analytically for normalization.
problem Estimating statistics of hidden units in neural networks for better initialization and normalization.
method Analytic moment propagation of mean and variance through the network structure.
result Analytic estimates of statistics are useful for initialization and normalization, independent of batch input.
Paper excludes the lowest energy level as an accumulation point for harmonic maps into analytic manifolds.
problem Analytic manifolds and their harmonic maps energy spectrum.
method Exclusion of the lowest energy level as an accumulation point using obstructions to the gluing of harmonic spheres and Lojasiewicz-estimates.
result Proves that the lowest energy level is not an accumulation point for generic 3-manifolds.
Estimates higher order derivatives using Lie derivatives and combinatorics.
problem Estimating higher order derivatives of Lie derivatives.
method Combines Lie derivatives, combinatorics of forests, and Dyck polynomials.
result Provides an estimate for higher order covariant derivatives of multiple Lie derivatives.
New method improves classification performance in Bayesian networks.
problem Estimating conditional probability tables in Bayesian networks.
method Hierarchical Multinomial-Dirichlet model for joint estimation of conditional distributions.
result Significantly improved classification performance compared to traditional methods.
Paper improves MMD estimation for analytical mean embeddings.
problem Improving MMD estimation for distributions with analytical mean embeddings.
method Proposes a tighter concentration result for MMD estimation under semi-explicit settings and extends to unbounded kernels.
result Demonstrates efficiency in real-world applications like index replication and calibration.
New formulas estimate life insurance benefits with less computation.
problem Estimating future discretionary benefits in life insurance.
method Derive analytic formulas for lower and upper bounds of FDB.
result Simple estimator for FDB with average of lower and upper bounds.
Gradient boosting estimates Riesz representer for causal inference.
problem Estimating causal quantities using traditional methods is challenging and prone to variance issues.
method Gradient boosting algorithm to directly estimate Riesz representer.
result Gradient boosting performs similarly or better than traditional methods in estimating causal quantities.
We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We intr…
Super-efficient automatic differentiation outperforms analytic methods in min-min optimization.
problem Optimizing functions defined as a minimum using iterative algorithms.
method Comparing automatic differentiation to analytic gradient estimation methods.
result Automatic differentiation yields an asymptotic error close to the square of the optimization error, demonstrating super-efficiency.
Study geometric and analytical properties of ρ-Einstein solitons.
problem Characterize geometric and analytical features of ρ-Einstein solitons. method Analyze the spectrum of the drifted Laplacian operator and prove volume growth estimates.
result Establish new volume growth estimates for geodesic balls of complete noncompact ρ-Einstein solitons. A new method improves density ratio estimation efficiency and accuracy.
problem Density ratio estimation trade-off between quality and efficiency.
method One-step Score-based Density Ratio Estimation (OS-DRE) combining analytic and solver-free approach.
result OS-DRE offers a favorable balance between estimation quality and inference efficiency.
Real analyticity proved for modified Laplacian coflow solutions.
problem Analyzing the modified Laplacian coflow on compact 7-manifolds.
method Improved Chen's Shi-type estimate to show real analyticity.
result The modified Laplacian coflow solution is real analytic.
Analytic networks with bounded coefficients can't outperform polynomial approximations.
problem Approximation limits of neural networks with analytic activation functions under coefficient constraints.
method Deterministic analysis using comparison argument and Bernstein-type estimates.
result Networks with analytic activation functions and controlled coefficients cannot outperform classical polynomial approximation rates on non-analytic targets.
Paper finds analytical solution for portfolio selection under worst-case model risk.
problem Portfolio optimization under model risk.
method Analytical solution for mean-variance portfolio selection in worst-case scenario.
result Analytical solution differs from previous numerical results, indicating model risk as estimation risk.
We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices …
We develop a new model and algorithms for machine learning-based learning analytics, which estimate a learner's knowledge of the concepts underlying a domain, and content analytics, which estimate the relationships among a collection of questions and those concepts. Our model represents the probability that a learner p…
Study shows relationship between Gini and Kolkata inequality indices.
problem Characterizing socio-economic inequality using Gini and Kolkata indices.
method Used both empirical data and analytical estimates to show the relationship.
result Significance of the relationship between Gini and Kolkata indices discussed.
New method for estimating gradients in stochastic binary networks.
problem Challenges in training neural networks with binary activations and weights.
method Combines sampling and analytic approximation steps to estimate gradients accurately.
result Significantly reduced variance at the cost of small bias, leading to practical tradeoffs.
ROI-driven data analytics guides investment in empirical data analysis.
problem Determining the optimal depth and breadth of data analytics.
method Conceptual framework validated through empirical studies focusing on dependency extraction in Mozilla Firefox project.
result ROI-driven data analytics helps avoid over-analyzing empirical data.
Study compares analytical and bootstrap DML confidence intervals across various machine learning algorithms.
problem Impact of machine learning algorithm choice on DML confidence intervals.
method Comprehensive simulation study comparing analytical and bootstrap DML confidence intervals across different machine learning algorithms.
result Substantial variability in coverage performance across analytical and bootstrap confidence intervals, highlighting the importance of learner choice.
Develops an analytical method for filtering point process observations.
problem Intractability of dynamic state estimation based on point process observations.
method Bayesian approximation to optimal filtering, introducing distributional assumptions.
result Analytic framework provides insights into optimal encoding strategies.
This paper improves uncertainty quantification in ELM models.
problem Uncertainty in ELM predictions due to data assumptions and randomness.
method Analytical derivations and variance estimates under various conditions.
result Improved understanding and estimation of ELM variability.
We study the estimation of β for the nonlinear model $y = f(X\sp{\top}β) + ε$ when f is a nonlinear transformation that is known, β has sparse nonzero coordinates, and the number of observations can be much smaller than that of parameters (n≪p). We show that in order to bound the L2 error of the L0 reg…
In this paper, we prove that if g(t) is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on M×[0,Ω], then the correspondence t↦g(t) is real-analytic at each t0∈(0,Ω). The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial …
OPAA estimates probability densities using functional analysis.
problem Estimating probability density functions efficiently and accurately.
method OPAA uses a parallelizable algorithm based on functional analysis to estimate probability distributions.
result OPAA provides an efficient method to estimate probability density functions and normalizing weights.
Study introduces a benchmark suite for evaluating neural MI estimators on real-world unstructured datasets.
problem Lack of comprehensive evaluation methods for neural MI estimators on real-world unstructured datasets.
method Developed a benchmark suite using same-class sampling and a binary symmetric channel trick.
result Showed accurate manipulation of true MI values of real-world datasets.
This paper uses Gaussian Process and converse Lyapunov function to estimate power system ROA.
problem Estimating the region of attraction (ROA) for power systems with conservative and limited analytical methods.
method Combining converse Lyapunov theorem and Gaussian Process to estimate ROA without needing an analytic Lyapunov function.
result The approach can significantly enlarge the estimated ROA compared to analytical methods.
Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning a…
The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing …
We use analytical and numerical methods to investigate the equations for cohomogeneity one shrinking gradient Ricci solitons. We show the existence of a winding number for this system around the subvariety of phase space corresponding to Einstein solutions and obtain some estimates for it. We prove a non-existence resu…
Survival analysis improves playtime measurement in games.
problem Measuring and improving player retention in games.
method Survival analysis for playtime data without covariates.
result Survival and hazard estimates provide a visual and analytic interpretation of playtime.
We show the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recentl…
Automatically improves Monte Carlo estimators in probabilistic programs.
problem Reducing variance in Monte Carlo estimators for probabilistic programs.
method Dynamic mechanism using conjugate priors and affine transformations.
result Automatic Rao-Blackwellization and locally-optimal proposals.
Proves heat expansion for Laplacian on a singularity.
problem Analytic hypersurface with isolated singularity and Laplacian heat expansion.
method Local parametrization, Newton scheme, quasihomogeneous tangent cone, local models with irregular singularities.
result Existence of small time heat expansion for Laplace operator.
In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The corresponding correlation matrix is constructed. It is found that the distribut…
We show that the classical Szasz analytic function SN(f)(x) is obtained by applying the pseudo-differential operator f(N−1Dθ) to the Bergman kernels for the Bargmann-Fock space. The expression generalizes immediately to any smooth polarized noncompact complete toric \kahler manifold, defining the generalized S…
Bayesian taut splines estimate modes in probability densities.
problem Estimating the number of modes in probability density functions.
method Bayesian inference with flexible kernel estimators and compositional splines.
result The new method provides more accurate results than traditional approaches.
Proves a smoothness estimate for complex Monge-Ampère solutions.
problem Estimating solutions to complex Monge-Ampère equations.
method Uses C2,α-estimate for solutions with specific smoothness conditions. result Proves C2,α estimate for complex Monge-Ampère solutions. In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. Th…
pmsims R package uses Gaussian process for flexible sample size estimation in clinical models.
problem Determining adequate sample size for clinical prediction models.
method Simulation-based Gaussian process search for flexible sample size estimation.
result Gaussian process-based method produces more stable sample size estimates, especially in challenging settings.
Analyzes transaction costs for corporate bonds using a new analytical methodology.
problem Challenges in assessing the quality of corporate bond executions via Transaction Cost Analysis.
method Analyzes TRACE Enhanced dataset to estimate initiator, bid-ask spread, and mid-price dynamics; applies regularized regression models and transient impact models.
result Identifies price impact asymmetry between customer-buy and consumer-sell orders.
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal encoding/decoding strategies, which are of significant relevance to Computational Neuroscien…
New estimator for smooth function estimation in high-dimensional Gaussian shift model.
problem Estimating smooth functions in high-dimensional Gaussian shift model.
method Fourier analytical approach to achieve effective bias reduction.
result Asymptotic normality and efficiency of the estimator for smoothness above a certain threshold.
The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.
problem Analyzing finite-time singularities in Spin(7)-structure flows.
method Proves Shi-type derivative estimates and shows that Λ(x,t) must blow up at finite-time singularities.
result Establishes a general analytic framework for studying Spin(7)-structure flows.