MKLpy simplifies Multiple Kernel Learning in Python.
problem Learning optimal kernel functions from data.
method Python-based framework for Multiple Kernel Learning algorithms.
result Maximizes usability and simplifies development of novel solutions.
The study finds the minimum number of critical points for functionals on Frechet spaces and Finsler manifolds.
problem Finding the minimum number of critical points for functionals on Frechet spaces and Finsler manifolds.
method Applying the Lusternik-Schnirelmann category to evaluate the minimal number of critical points for Keller Cc1-functionals on Frechet spaces and Finsler manifolds. result The minimal number of critical points is determined by the Lusternik-Schnirelmann category.
Algorithm finds function contours using multiple approximations.
problem Locating contours of expensive-to-evaluate functions.
method Uses multiple biased and noisy approximations to locate contours efficiently by maximizing entropy reduction.
result Maximizes reduction of contour entropy per unit cost.
We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current; we derive explicit formulae for the boundary, the mass and the first variations a…
We show that there is no analog of Kirszbraun's extension theorem for Almgren's multiple valued functions.
s-RBFN integrates multiple hypotheses for efficient and diverse prediction.
problem Integrating multiple hypotheses into learning models for regression.
method Structured Radial Basis Function Network (s-RBFN) using Voronoi tessellations and least-squares training.
result s-RBFN achieves superior generalization and efficiency compared to other models.
Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. This leads either to an inefficient distribution of computational resources or an extensive increase in the comput…
Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. However, this leads to an extensive increase in the computational complexity of the training procedure. We present…
We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.
Paper proves multiplicative weight updates can train neural networks without learning rate tuning.
problem Vanishing and exploding gradients in gradient descent for compositional functions.
method Proves descent lemma for compositional functions using multiplicative weight updates and derives Madam optimizer.
result Madam optimizer trains state-of-the-art neural networks without learning rate tuning.
A novel procedure detects outliers in functional data using multiple testing.
problem Outlier detection in functional data.
method Multiple testing based on two-sample test on coefficients of functional data projected onto orthonormal bases.
result Selected coefficients as features for outlier detection using Local Outlier Factor.
For functions of a single complex variable, points of multiplicity greater than k are characterized by the vanishing of the first k derivatives. There are various quantitative generalizations of this statement, showing that for functions that are in some sense close to having multiplicity greater than k, the firs…
Paper studies fractional CR Yamabe equation on sphere, proving multiplicity of solutions.
problem Fractional CR Yamabe equation on sphere solutions.
method Analyzed Palais-Smale sequences to characterize bubbling phenomena and prove multiplicity of solutions.
result Existence of infinitely many solutions to the fractional CR Yamabe equation.
Study shows strong multiplicity one property for 3D hyperbolic spaces.
problem Understanding the spectrum of length-holonomy in 3D hyperbolic spaces.
method Analyzing Selberg-Gangolli-Wakayama zeta functions.
result Established a strong multiplicity one type property for length-holonomy spectrum.
New sampling-based approach for filtering problems using multiplicative Gaussian functions.
problem Approximate inference in filtering problems.
method Approximates distribution with a weighted sum of continuous functions using sampling for multiplications.
result Preliminary experiments show potential of the new method compared to particle filters.
The paper studies complex genera and related geometric applications, deriving formulas for multiple zeta values.
problem Understanding coefficients in Chern numbers for complex genera.
method Examining Chern numbers for complex genera, focusing on specific genera like Td^(1/2), Γ, and Todd.
result Unified formulas for multiple zeta values and transition matrices among symmetric functions.
Flexible VHDL design for multiple neural networks on FPGAs.
problem Inflexible neural network designs for FPGAs.
method Proposes a flexible VHDL structure with multiple processor groups.
result Allows training and testing of multiple neural networks on multiple FPGAs.
New method learns multiple reward functions for complex tasks.
problem Learning reward functions for tasks with multiple ways of solving.
method Combines maximum entropy approach with Dirichlet process clustering.
result Method accurately learns reward functions for complex tasks.
The purpose of this paper is to present the construction of a canonical determinant functional on elliptic pseudodifferential operators associated to the Guillemin-Wodzicki residue trace. The resulting functional is multiplicative, a local invariant, and not defined by a regularization procedure. The residue determinan…
Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.
problem Understanding the multiplicity of non-acyclic SL2-representations and their L-functions.
method Geometric interpretation of Reidemeister torsion divisors and application to L-functions.
result Prove multiplicity two for odd-twisted Whitehead links.
Study introduces a new method for multiple parameter regularization in polynomial functional regression.
problem Handling varying regularization parameters in polynomial functional regression.
method Developed a theoretically grounded algorithm for multiple parameter regularization and model aggregation.
result Promising results from evaluations on synthetic and real-world data.
SrvfNet aligns multiple functional data to templates without supervision.
problem Aligning large collections of functional data to templates without labeled data.
method Generative deep learning framework using SRVF and fully-connected layers.
result Framework achieves alignment and optimal template prediction without supervision.
Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set of irreducible representations of G. Let T be a maximal torus of G with Lie algebra Lie(T). We construct a finite number of piecewise polynomial …
Study on multiple linking numbers, extending Gauss diagram formulas.
problem Extending link invariants to more complex diagrams.
method Investigate second Gauss diagram formula involving two arrows.
result Discover two types of multiple linking numbers, one Vassiliev invariant, the other sensitive to Reidemeister moves.
We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generaliz…
Left-symmetric algebras help define affine spheres.
problem Characterizing improper affine spheres in flat affine space.
method Analyzing left-symmetric algebras and their properties.
result Conditions for left-symmetric algebras to yield proper affine spheres.
Constructs new elicitable risk measures with multiplicative scoring functions.
problem Defining new elicitable risk measures with specific properties.
method Constructs new elicitable risk measures using a multiplicative scoring function.
result Encompasses and allows construction of novel elicitable risk measures.
This paper uses random Fourier features to simplify latent force models and convolved Gaussian processes.
problem Expensive covariance matrix calculation in latent force models due to double integrals.
method Approximates double integrals using random Fourier features to obtain simpler analytical expressions.
result Simplified analytical expressions for covariance functions, leading to faster computation.
Revisits and proves a reparametrization theorem for multi-valued graphs in higher codimension.
problem Analyzing multi-valued sections of vector bundles and proving a reparametrization theorem.
method Develops properties of Q-multisections and provides a geometric proof. result Elementary and purely geometric proof of a reparametrization theorem for multi-valued graphs.
By the method of discrete Morse flows, we construct an energy reducing multiple-valued function flow. The flow we get is Holder continuous with respect to the L-2 norm. We also give another way of constructing flows in some special cases, where the flow we get behaves like ordinary heat flow.
The paper shows how utility indifference prices approach superreplication prices in uncertain markets.
problem Modeling investor preferences under non-dominated uncertainty.
method Formulates and proves convergence of utility indifference prices to superreplication prices.
result Utility indifference prices converge to superreplication prices under certain conditions.
We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of principal curves and introduce a new functional which allows for multiple curve…
The existence of Dirichlet minimizing multiple-valued functions for given boundary data has been known since pioneering work of F. Almgren. Here we prove a multiple-valued analogue of the classical Plateau problem of the existence of area-minimizing mappings of the disk. Specifically, we find, for K∈N, $k…
Efficiently prices American options with multiple assets using sparse grids.
problem Pricing American options with multiple underlying assets efficiently.
method Dynamic programming formulation followed by sparse grid interpolation.
result Sparse grids reduce the number of interpolation points and maintain function smoothness.
The moments of historic stock returns align with the Heston model, not the multiplicative model.
problem Understanding the distribution of historic stock returns and volatility.
method Comparison of moments with Heston and multiplicative models, analysis of mean realized variance.
result The moments of historic stock returns are better explained by the Heston model than the multiplicative model.
In this paper we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the epsilon-Dirichlet problem obtained as a variational problem for the SU(2)-epsilon-Yang Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem fo…
A multiple instance dictionary learning method using functions of multiple instances (DL-FUMI) is proposed to address target detection and two-class classification problems with inaccurate training labels. Given inaccurate training labels, DL-FUMI learns a set of target dictionary atoms that describe the most distincti…
This paper tackles deferral learning with multiple experts, providing strong theoretical guarantees.
problem Optimizing input assignment to experts balancing accuracy and computational cost.
method Introducing new surrogate loss functions and efficient algorithms with strong theoretical learning guarantees.
result Realizable H-consistency, H-consistency bounds, and Bayes-consistency for deferral learning. Framework benchmarks optimizers on multiple criteria.
problem Benchmarking optimizers across diverse test functions.
method Union-free generic depth function for partial orders/rankings.
result Identifies central and outlying rankings of optimizers.
Study on learning to defer with multiple experts using new surrogate losses.
problem Learning to defer with multiple experts in a machine learning context.
method Introducing a new family of surrogate losses for the multiple-expert setting, proving H-consistency bounds, and designing learning algorithms. result Explicit guarantees for new learning to defer algorithms based on minimization of these surrogate losses.
The paper tackles learning smooth distance functions using query-based methods.
problem Learning smooth distance functions under query constraints.
method Global and local approaches using Mahalanobis distance functions.
result Quadratic query complexity for both additive and multiplicative approximations.
Geometric pruning rules improve change point detection in multiple time series.
problem Detecting multiple changes in multiple independent time series.
method Dynamic programming algorithms with inequality-based and geometric pruning rules.
result Geometric pruning rules offer close-to-linear time complexity for multiple independent time series.
Tree-based algorithm for functional data analysis reduces generalization error.
problem Classification and regression problems with functional data.
method Constrained convex optimization for weighted functional L2 space, multiple splitting rules, and weighted integral features. result Reduces generalization error while maintaining interpretability.
A new method clusters subjects based on brain networks without vectorizing fMRI data.
problem Distortion of clustering results when simplifying fMRI data structure.
method Wishart mixture models for multiple-view clustering of brain networks.
result Identifies multiple underlying pairs of associations between subject clusters and brain sub-networks.
A new method selects multiple activation functions at each layer of a neural network.
problem Selecting an adequate activation function requires trial and error.
method Activation Ensembles: introduces additional variables α to allow for multiple activation functions at each neuron. result Achieves superior results compared to traditional techniques.
This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. Recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples. This study examines Ridge Support Vector Models, subsequently devising a recursion-…
Study tackles RLHF with diverse human feedback, showing limitations and proposing a meta-learning approach.
problem Traditional RLHF fails to balance diverse human preferences.
method Integrates meta-learning and multiple social welfare functions to optimize diverse preferences.
result Establishes sample complexity bounds for optimizing diverse social welfare functions.
New method recovers latent sources from multiple noisy views using deep neural networks.
problem Recovering a common latent source from multiple nonlinearly mixed views.
method Novel identifiability proofs using deep neural networks.
result Independent latent sources can be recovered from multiple noisy views using deep neural networks.