Study reduces discrete mechanical systems using Lagrangian methods.
problem Discrete mechanical systems and their symmetries.
method Introduce LP_d category, study properties, define symmetry groups, reduction procedure.
result Two-step reduction isomorphic to full reduction under certain conditions.
Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.
problem Analyzing errors in high-dimensional regression with dimensionality reduction and kernel regression.
method Derive a stability result for kernel regression with Wasserstein distance and apply it to PCA to deduce convergence rates.
result Two-step procedure yields useful convergence rates in semi-supervised settings.
Paper reduces nonholonomic systems with symmetries.
problem Nonholonomic systems with symmetries and conserved quantities.
method Two-step reduction procedure: first results in Chaplygin system, second in almost symplectic structure.
result Almost symplectic manifolds coincide with reduced nonholonomic brackets.
The paper tackles manifold overfitting in deep generative models.
problem Manifold overfitting occurs when generative models learn the manifold itself instead of the distribution on it.
method The authors propose a two-step procedure: dimensionality reduction followed by maximum-likelihood density estimation.
result The two-step procedure avoids manifold overfitting and enables density estimation on learned manifolds.
This paper merges deterministic policy gradient estimations to improve deep reinforcement learning performance.
problem The bias-variance tradeoff in estimating and using policy gradients for deep reinforcement learning.
method Introduces elite policy gradients and a two-step merging method to balance bias-variance tradeoffs.
result Two-step merging outperforms interpolation merging and state-of-the-art algorithms on benchmark control tasks.
Proposes efficient subsampling for logistic regression with optimal probabilities.
problem Efficiently approximating maximum likelihood estimate in logistic regression for large datasets.
method Develops subsampling algorithms for logistic regression, derives optimal subsampling probabilities, and proposes two-step approximation.
result Optimal subsampling reduces computing time significantly while maintaining estimator consistency and normality.
The paper shows how to recover true node positions from a graph or similarity matrix.
problem Recovering true distances and positions from a graph or similarity matrix.
method Two steps: matrix factorisation followed by nonlinear dimension reduction.
result Nonlinear dimension reduction can recover latent positions close to a manifold where geodesic distance is encoded.
Study high-dimensional covariance matrix estimators for complex portfolios, improving financial metrics.
problem Estimating covariance matrices in high-dimensional portfolios with nested and one-factor structures.
method Combining random matrix theory, free probability, deterministic equivalents, and two-step covariance estimators.
result Two-step estimators improve financial metrics in complex and one-factor covariance models.
Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and p…
A 2-step nilpotent Lie algebra n is called nonsingular if ad(X): n --> [n,n] is onto for any X not in [n,n]. We explore nonsingular algebras in several directions, including the classification problem (isomorphism invariants), the existence of canonical inner products (nilsolitons) and their automorphism groups (maxima…
A method for high-dimensional Bayesian optimization reduces dimensionality using EDR and Gaussian process.
problem Extending Bayesian optimization to high-dimensional settings.
method Two-step framework: EDR subspace identification followed by Gaussian process optimization.
result Algorithm converges in high-dimensional contexts, validated by numerical experiments.
The paper extends two-step homogeneous geodesics to homogeneous Finsler spaces.
problem Extending two-step homogeneous geodesics to Finsler spaces.
method Providing sufficient conditions for (α,β) spaces and decomposable cubic spaces to have two-step Finsler geodesic orbit spaces. result Presented examples of two-step Finsler geodesic orbit spaces.
Classifies two-step solvable Lie groups with SKT structures.
problem Classifying Lie groups with SKT structures.
method Shear construction and analysis of SKT shear data on Abelian Lie algebras.
result Large part of the classification for two-step solvable SKT algebras of dimension six.
New kernels allow learning from non-separable data.
problem Learning from non-separable data.
method Introducing entangled kernels and a two-step algorithm.
result Efficient algorithm for learning entangled kernels.
We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the graphs from which they arise are isomorphic.
Paper introduces new actuarial-consistent valuations for insurance liabilities.
problem Valuation of insurance liabilities considering both financial and actuarial risks.
method Proposes two-step actuarial valuations and actuarial-consistent procedures.
result Actuarial-consistent valuations are equivalent to two-step actuarial valuations under coherence.
This work improves chemistry modeling by jointly learning reaction progress variables and look-up models.
problem Jointly modeling turbulent combustion requires solving both chemistry and flow systems simultaneously, which is computationally expensive.
method Developed a deep neural network architecture that jointly learns reaction progress variables and look-up models, improving accuracy.
result Joint learning yields more accurate results in chemistry modeling.
Proves conjecture about compatible SKT and balanced metrics on compact solvmanifolds.
problem Compact complex manifolds with both SKT and balanced metrics.
method Shear construction and classification of two-step solvable Lie algebras.
result Proves conjecture for compact two-step solvmanifolds with invariant complex structures.
The paper analyzes portfolio credit risk using Archimedean copulas and introduces efficient simulation methods.
problem Analyzing large losses from credit portfolio defaults with Archimedean copulas.
method Derives asymptotic results and develops variance reduction algorithms for Monte Carlo simulations.
result Proposed algorithms significantly enhance classical Monte Carlo methods for estimating portfolio credit risk.
GAMs combine autoregressive and log-linear components for data-efficient sequence learning.
problem Poor performance of standard autoregressive models under small-data conditions.
method Introduce Global Autoregressive Models (GAMs) combining autoregressive and log-linear components, trained in two steps.
result GAMs show a strong perplexity reduction over standard models in language modelling.
A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite a substantial pr…
Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challeng…
Parametric UMAP learns a mapping from data to embeddings.
problem Representing and learning from structured data.
method Parametric optimization over neural network weights for UMAP.
result Parametric UMAP performs comparably to non-parametric UMAP with faster online embeddings.
We associate a two-step nilpotent Lie algebra to an arbitrary Schreier graph. We then use properties of the Schreier graph to determine necessary and sufficient conditions for this Lie algebra to extend to a three-step nilpotent Lie algebra. As an application, if we start with pairs of non-isomorphic Schreier graphs co…
Proves measure contraction for specific sub-Riemannian structures.
problem Measure contraction properties in sub-Riemannian structures.
method Analytic sub-Riemannian structures and Lipschitz Carnot groups.
result Proves measure contraction properties for the structures.
A two-step nonparametric method estimates financial systemic risk.
problem Estimating CoVaR due to unobservability of multivariate-quantiles.
method Two-step nonparametric approach using Monte-Carlo simulation and kernel method.
result Consistency and asymptotic normality of the two-step estimator established.
A new method reduces speckles in high contrast imaging.
problem Over-subtraction from speckles and self-subtraction in data reduction.
method Data Imputation concept using Karhunen-Loève transform (DIKL).
result DIKL achieves high-quality results with significantly reduced computational cost.
Many mathematical models of physical phenomena that have been proposed in recent years require more general spaces than manifolds. When taking into account the symmetry group of the model, we get a reduced model on the (singular) orbit space of the symmetry group action. We investigate quantization of singular spaces o…
A conjugate Bayesian method detects change points in Hawkes processes efficiently.
problem Non-conjugacy between Hawkes process likelihood and prior causes inefficiency in change point detection.
method Data augmentation to propose a conjugate Bayesian two-step change point detection method.
result The conjugate method is more accurate and efficient than non-conjugate methods.
A new two-step LSMC method improves game option pricing accuracy.
problem Improving game option pricing accuracy using Monte Carlo methods.
method Proposed a two-step Longstaff Schwartz Monte Carlo approach with two regression models fitted at each time step.
result Our method produces more reliable results compared to the original LSMC.
Two-step process generates molecules from latent vectors.
problem Generating valid molecules from latent representations.
method Two-step decoding: first formula, then bonds.
result Highest reconstruction rate of 90.5%.
Two-step conformal prediction method for adaptive bounding box uncertainties in multi-object detection.
problem Quantifying predictive uncertainty for multi-object detection in safety-critical applications.
method Developed a two-step conformal prediction approach to propagate uncertainty in predicted class labels into bounding box uncertainties, ensuring coverage for incorrectly classified objects.
result Desired coverage levels are satisfied with practically tight predictive uncertainty intervals on real-world datasets.
A new two-step MH method for Bayesian EL computation.
problem Complex likelihood support in Bayesian EL.
method Hierarchical Metropolis Hastings with reversible jump MCMC.
result Improved sampling from BayesEL posteriors.
The paper discusses a new method for constructing two-step Darboux transforms of isothermic surfaces.
problem Constructing two-step Darboux transforms of isothermic surfaces.
method Sym-type construction using parallel sections of the associated family.
result All two-step Darboux transforms of an isothermic surface are given without further integration.
A new Bayesian method optimizes time-dependent expensive functions with lookahead.
problem Maximizing a time-dependent, expensive oracle with limited evaluations.
method Recursive, two-step lookahead expected payoff (r2LEY) acquisition function.
result r2LEY outperforms myopic methods in synthetic and real-world datasets.
We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We prop…
Simplified Khovanov-Rozansky operators for link invariants.
problem Complexity in Khovanov-Rozansky knot invariants.
method Substituted matrix factorization with simple operators and conjugations.
result Global reductions for simplifying link invariants.
The paper extends risk measures to two-step approximations and studies log-concave distributions.
problem Extending classical risk measures to two-step approximations.
method Optimization problem for determining optimal regime thresholds and values for log-concave distributions.
result Conditions for the uniqueness of regime changing in log-concave distributions.
The paper studies time-optimal problems on specific Lie groups, describing orbits and integrals.
problem Time-optimal control problems on two-step Carnot groups.
method Description of co-adjoint orbits, Casimir functions, and integrals for the Hamiltonian system.
result Characterization of the flow and constancy of solutions for two-dimensional co-adjoint orbits.
The paper discusses polynomial convergence to conical Kähler-Einstein metrics.
problem Understanding the convergence of Kähler-Einstein metrics to conical structures.
method Two-step degeneration theory and algebraic singularity analysis.
result Singular Kähler-Einstein metrics are conical if curvature grows quadratically near a point.
We simplify Volterra process predictions by reducing dimensionality and using a tailored deep learning model.
problem Predicting the conditional law of Volterra processes with stochastic volatility is challenging due to high dimensionality and non-smoothness.
method We developed a stable dimension reduction technique onto a low-dimensional statistical manifold of non-positive curvature and introduced a sequentially deep learning model tailored to this geometry.
result Our model can approximate the conditional law of Volterra processes with approximation rates achievable only with very large networks.
New method for insurance valuation combining hedging and risk minimization.
problem Current insurance valuation methods do not reflect regulatory risk measures.
method Two-step hedging procedure using generalised regression.
result The method produces portfolios neutral to risk measures like VaR or expectiles.
Paper reduces neural network complexity for image classification.
problem High computational complexity in deep neural networks.
method Proposes a two-step classification process: coarse-grain and fine-grain.
result Achieves similar accuracy with less computational complexity.
New methods use vector search and nearest-neighbor matching for policy learning in causal inference.
problem Learning optimal policies in causal inference with limited data.
method RAG-based policy learning with vector search and nearest-neighbor matching.
result The methods bound the within-candidate choice regret and evaluate the one-step method directly as a policy.
We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common measurements of the columns. In the second step, the subspace aware recovery of …
A simple two-step procedure yields valid inference in high-dimensional linear models.
problem Valid inference in high-dimensional linear models with lasso selection.
method Two-step procedure: lasso followed by least squares on lasso-selected variables.
result The set of variables selected by the lasso is deterministic and can be used for valid inference.
In this paper we study the geometry of simply connected two-step nilpotent Lie groups of dimension five. We give the Levi-Civita connection, curvature tensor, sectional and scalar curvatures of these spaces and show that they have constant negative scalar curvature. Also we show that the only space which admits left in…
Proposes a two-step method for sound source separation.
problem Improving sound source separation performance.
method First, learn a latent space transform. Second, train a separation module in the latent space.
result The proposed method achieves better performance than joint learning approaches.