Reduces function approximation dimensions from high to low with sparse data.
problem Function approximation from sparse data.
method Nonlinear Level Set Learning (NLL) with geometric information.
result Reduces input dimension to theoretical lower bound with minor accuracy loss.
SBS policy improves crypto market forecasts by 0.15% with minimal model changes.
problem Improving crypto market forecasting models while minimizing model state transitions.
method Shadow Before Swap (SBS) policy that warm-refits and evaluates challenger models.
result Reduces NLL by 0.1472% relative to continuous maintenance in historical data.
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…
Enhances ENet's prediction accuracy while maintaining uncertainty estimation.
problem Gradient shrinkage problem in ENet's loss function.
method Proposes a multi-task learning framework with a modified MSE loss function.
result Improves ENet's prediction accuracy without losing uncertainty estimation.
Smooth neural TPPs using B-splines for better efficiency and accuracy.
problem Efficiently modeling sequences of events in continuous time with neural networks.
method Directly parametrize the CIF as a non-negative combination of B-spline basis functions, predicting coefficients with a neural network.
result Improved computational efficiency and predictive accuracy compared to existing methods.
ICAL improves deep learning model accuracy and NLL with optimized batch labeling.
problem Deep Bayesian Active Learning for efficient model training.
method ICAL uses HSIC to measure dependency and optimizes batch size scaling.
result Significant improvements in model accuracy and NLL on image datasets.
Proposes integrating random effects into deep neural networks for better predictive performance.
problem Correlated data in real-life applications are not handled well by traditional deep neural networks.
method Uses mixed models with random effects to handle correlations in deep neural networks, minimizing Gaussian negative log-likelihood with SGD.
result Improves predictive performance over natural competitors in various correlation scenarios.
Post-hoc calibration of neural networks using g-Layers proves theoretical justification.
problem Ensuring the confidence of neural network decisions in real-world applications.
method Proves theoretical justification for post-hoc calibration methods by adding g-Layers and minimizing NLL.
result Proves that adding g-Layers and minimizing NLL can lead to a calibrated network.
JUCAL jointly calibrates aleatoric and epistemic uncertainties in classifier ensembles.
problem Misrepresentation of predictive uncertainty due to unbalanced aleatoric and epistemic uncertainties.
method Joint Uncertainty Calibration (JUCAL) that jointly calibrates two constants to weight and scale uncertainties.
result Significantly outperforms state-of-the-art calibration methods across various text classification tasks.
The log-likelihood loss in heteroscedastic neural networks can lead to poor parameter estimates.
problem Capturing aleatoric uncertainty in deep learning models.
method Examine the log-likelihood loss in conjunction with gradient-based optimizers and propose an alternative formulation, β-NLL. result Using an appropriate β largely mitigates the issue of poor parameter estimates. New method trains energy-based models faster and more stably.
problem Training efficiency and stability of energy-based models.
method EBFlow with score-matching objectives.
result EBFlow achieves significant speedup and better performance.
Estimates uncertainty in bounding box regression for object detection.
problem Reliable deployment of deep object detectors in safety-critical tasks.
method Training variance networks with energy score as a proper scoring rule.
result Energy score leads to better calibrated and lower entropy predictive distributions.
ProbFM provides principled uncertainty quantification for financial forecasting.
problem Lack of principled uncertainty quantification in financial applications.
method Probabilistic Time Series Foundation Model with Uncertainty Decomposition using Deep Evidential Regression (DER).
result DER maintains competitive forecasting accuracy while providing explicit epistemic-aleatoric uncertainty decomposition.
A new method normalizes flow mixtures for better inference across different data types.
problem Inference failure across diverse posterior geometries in normalizing flows.
method Introduces a two-stage framework with a stable global weighting mechanism based on sEMA.
result Achieves consistent NLL improvements and stable weight trajectories over baselines.
A new method speeds up uncertainty estimation in image classification.
problem Fast and accurate uncertainty estimation for robust robotics applications.
method Deep sub-ensembles, where only layers close to the output are ensembled.
result Significant speedup in uncertainty estimation with minimal error and NLL increase.
DNLL loss improves deep LDA accuracy and consistency.
problem Pathological solutions in unconstrained Deep LDA.
method Introducing Discriminative Negative Log-Likelihood (DNLL) loss.
result Deep LDA trained with DNLL produces clean latent spaces and better calibrated probabilities.
This paper proves the necessity and effectiveness of learning the prior in VAEs.
problem Aggregated posterior may not match unit Gaussian prior, leading to poor variational inference.
method Proves necessity and effectiveness of learning the prior, analyzes why it's needed, and proposes hypothesis.
result Learning the prior can improve reconstruction loss and achieve comparable test NLL to deep hierarchical VAEs.
UTS improves DNN uncertainty calibration without labels, robust to domain shift.
problem Improving uncertainty calibration of DNNs under domain shift.
method UTS uses unlabeled test samples and a novel weighted NLL loss function.
result UTS outperforms other methods in domain shift scenarios.
New method uses interval-based metric to validate prediction uncertainty in machine learning.
problem Validation of prediction uncertainty in machine learning regression tasks is unreliable due to heavy-tailed distributions.
method Shift from variance-based metrics to interval-based Prediction Interval Coverage Probability (PICP).
result PICP method more quickly and reliably tests prediction intervals than variance-based metrics.
This work evaluates uncertainty in deep Gaussian processes.
problem Uncertainty quantification in deep Gaussian processes.
method Hierarchical deep Gaussian processes (DGPs) and Deep Sigma Point Processes (DSPPs) evaluated on regression and classification tasks.
result DSPPs provide strong in-distribution calibration but are less robust under distribution shift compared to ensembles.
This work tackles the challenge of aligning generative models without explicit reward signals.
problem Aligning generative models without explicit reward signals.
method A Bilevel Optimization framework where the reward function is treated as the optimization variable of an outer-level problem.
result Theoretical analysis and insights generalize to tabular classification and model-based reinforcement learning.
Paper proposes a new loss function for conditional models using soft targets.
problem Improving generalization performance of deep neural networks on supervised classification tasks.
method Introduces a new loss function compatible with soft targets, based on noise contrastive estimation.
result Soft target InfoNCE loss performs on par with cross-entropy baselines and outperforms other losses.
Develops a theoretical framework for scalable Gaussian Process regression methods.
problem Limited scalability of Gaussian Process regression for large datasets.
method Introduces and analyzes Nearest Neighbour Gaussian Process (NNGP) and scalable GPnn methods.
result Derives almost sure pointwise limits for predictive criteria and proves risk minimax rates.
New GPnn method achieves scalable regression with low computational cost.
problem Inefficient Gaussian Process (GP) regression for large datasets.
method GP nearest-neighbour (GPnn) prediction with robustness and limiting behaviour exploration.
result GPnn achieves high MSE accuracy with minimal parameter estimation effort, even in gross misspecification.
Volatility is a quantity of measurement for the price movements of stocks or options which indicates the uncertainty within financial markets. As an indicator of the level of risk or the degree of variation, volatility is important to analyse the financial market, and it is taken into consideration in various decision-…
This research explores discrete diffusion models for natural language generation.
problem Challenges in applying diffusion models to discrete data, especially natural language.
method Investigates Discrete Denoising Diffusion Probabilistic Model (D3PM) and compares it with autoregressive models.
result Discrete diffusion models achieve better processing speed than autoregressive models.
This paper identifies knot projections with reductivity two.
problem Determining knot projections with a specific reductivity level.
method Examined four types of reductivity (Seifert type splice, non-Seifert type splice, recursively, simultaneously) and their combinations.
result Identified all knot projections with reductivity two for the four definitions.
Completes reduction scheme in Lagrange-Poincaré category.
problem Lagrangian reduction by stages in the whole category.
method Analyzes Noether theorem, Hamiltonian reduction, geometric aspects.
result Affirmative answer to open question of Lagrangian reduction.
This paper classifies instantons with closed reductions and provides examples of non-closed reductions.
problem Understanding the geometry of toric Kähler instantons with and without closed reductions.
method Sharp geometric criteria and examples of instantons with different reduction types.
result Established geometric criteria for closed reductions and classified asymptotic geometries.
We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,Γ) where K is a Kaehler manifold and Γa discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invari…
In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We sh…
Two reduction schemes for symplectic manifolds are shown equivalent.
problem Reduction of Hamiltonian systems on exact symplectic manifolds.
method Modified Marsden-Meyer-Weinstein reduction theorem for exact symplectic manifolds and contact manifolds.
result Reduction schemes are equivalent for exact symplectic manifolds and energy hypersurfaces.
Study extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.
problem Existence of compact Clifford-Klein forms in homogeneous spaces.
method Extend Kobayashi's method to non-reductive subgroups and compare Cartan projections and non-compact dimensions.
result Examples of homogeneous spaces without compact Clifford-Klein forms.
The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reduction.
We show that the contact reduction can be specialized to Sasakian manifolds. We link this Sasakian reduction to Kähler reduction by considering the Kähler cone over a Sasakian manifold. We present examples of Sasakian manifolds obtained by S1 reduction of standard Sasakian spheres.
Study characterizes naturally reductive metrics on homogeneous manifolds.
problem Characterizing naturally reductive (α1,α2) metrics on homogeneous manifolds. method Characterization through local f-products and equivalence of properties. result Explicit flag curvature formula for naturally reductive metrics.
Abstract: Generalized reduction methods for symmetries in graded geometry.
problem Generalized reduction of symmetries in graded geometry.
method Graded symplectic reduction for Courant, Dirac, and generalized complex structures.
result Systematic recovery of reduction schemes for exact cases.
In this note we give conditions which ensure the reduction of a symplectic connection in the process of a Marsden-Weinstein reduction and of the reduction of a presymplectic manifold.
This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to descr…
This paper extends symplectic reduction to cosymplectic groupoids and explores their properties.
problem Cosymplectic groupoids and their reductions.
method Analogous to symplectic reduction, the authors extend the Marsden-Weinstein-Meyer reduction to cosymplectic groupoids.
result Integration commutes with reduction for algebroids associated with cosymplectic groupoids.
The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.
Let EG be a stable principal G--bundle over a compact connected Kaehler manifold, where G is a connected reductive linear algebraic group defined over the complex numbers. Let H⊂G be a complex reductive subgroup which is not necessarily connected, and let EH⊂EG be a holomorphic reduction of s…
A new method for classifying naturally reductive spaces is presented. This method relies on the structure theory of naturally reductive spaces developed in \cite{Storm2018a} and the new construction of naturally reductive spaces in \cite{Storm2018}. We obtain the classification of all naturally reductive spaces in dime…
New definition of naturally reductive Finsler manifolds using geodesic graphs.
problem Defining naturally reductive Finsler manifolds using geodesic graphs.
method Proposed a new geometrical definition using geodesic graphs and constructed examples of Finsler metrics.
result Explicit examples of Finsler naturally reductive metrics constructed.
Survey of Lagrangian reduction for discrete mechanical systems.
problem Understanding and reducing complex mechanical systems.
method Lagrangian reduction applied to discrete-time mechanical systems.
result Introduction to reduction techniques for various constraints and forces.
New method corrects missing data bias in dimension reduction.
problem Missing data complicates high-dimensional data analysis.
method Developed a bias-corrected Gram matrix for heterogeneous missingness.
result Proposed method improves dimension reduction techniques significantly.
Paper compares Lagrangian reduction methods for rigid body systems.
problem Modeling and reduction of rigid body systems with rotors.
method Euler-Poincaré reduction by the whole group and reduction by stages.
result Equivalence of equations and conservation laws are tracked.
The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.
problem Limitations of Marsden-Weinstein reduction for cosymplectic structures in time-dependent Hamiltonian systems.
method Developed Marsden-Weinstein reduction for mechanical presymplectic structures.
result Mechanical presymplectic structures provide a more suitable framework for time-dependent Hamiltonian systems than cosymplectic structures.