Paper extends trigonometric summation formula with weights.
problem Trigonometric summation formula by Grigor'yan, Lin and Yau.
method Weighted trigonometric summation formula derivation.
result Extension of trigonometric summation formula.
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48 results for “Weighted Sum”
Paper introduces new approximations for lognormal sums, matching comonotonicity and moments.
problem Approximating sums of lognormal random variables accurately.
method Introduces new approximations based on weighted distribution theory, emphasizing comonotonicity and moment matching.
result Approximations perform better than classical methods, especially in the right tail of the distribution.
Jones polynomials compute weighted sums of Lefschetz numbers.
problem Computing Lefschetz numbers for braids.
method Colored Jones polynomials of braid closures.
result Jones polynomials compute abelianized Lefschetz numbers.
LSTMs are explained as a weighted sum of context-independent functions.
problem Vanishing gradients in simple RNNs.
method Decouple LSTM gates from simple RNNs, computing an element-wise weighted sum of context-independent functions.
result Gating mechanism alone performs as well as an LSTM in most settings, suggesting more representational power.
The paper develops concentration inequalities for structured random data, extending beyond independent terms.
problem Developing concentration inequalities for structured weighted sums of random data, including tensors and matrix-valued data.
method The paper develops Hoeffding and Bernstein bounds for structured weighted sums under exchangeability, extending beyond the classical framework of independent terms.
result The paper develops a sharper concentration bound for combinatorial sums of matrix arrays.
Sharp bounds for Dirichlet sums lead to improved Bayesian algorithm analysis.
problem Improving Bayesian algorithm performance through precise deviation bounds.
method Novel integral representation of Dirichlet sum density, Gaussian approximation, complex analysis.
result Significantly sharpened regret bounds for Multinomial Thompson Sampling.
ZeroS improves Transformers by adding negative weights, matching or beating softmax attention.
problem Limited performance of linear attention methods, especially in long context sequences.
method Proposes Zero-Sum Linear Attention (ZeroS) that removes the zero-order term and reweights zero-sum softmax residuals.
result ZeroS matches or exceeds standard softmax attention across various benchmarks, theoretically expanding representable functions.
Develops a Bayesian non-parametric approach for signal separation with varying components.
problem Signal separation with varying components across different input locations.
method Augments Gaussian Process Latent Variable Models with weighted sums of pure component signals and incorporates priors for linear weights.
result Framework allows for non-linear variations in signals and incorporates useful priors for linear weights.
This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…
G-FIGS uses instance weights to create interpretable models from diverse data.
problem Generalizing to diverse data distributions while maintaining interpretability.
method Estimates group membership probabilities, uses as instance weights in FIGS to grow decision trees.
result Achieves state-of-the-art prediction performance and maintains interpretability.
NESTA accelerates neural networks by compressing Hamming weights.
problem Efficiently computing convolution layers in deep neural networks.
method NESTA reformats convolutions into batches and uses Hamming Weight Compressors to process each batch, approximating partial sums and adding residuals.
result Significantly speeds up convolution computations with reduced energy consumption.
The paper proves an asymptotic development for weighted sums of multiplicity functions on a torus-manifold.
problem Proving an asymptotic development for weighted sums of multiplicity functions on a torus-manifold.
method Using equivariant Riemann-Roch theorem and graded Todd class, the paper proves an asymptotic development for weighted sums of multiplicity functions on a torus-manifold.
result The weighted sum of multiplicity functions has an asymptotic development in terms of the twisted Duistermaat-Heckman distributions associated to the graded Todd class of M.
New method preserves privacy by aggregating feature-vectors with weighted sums, ensuring label differential privacy.
problem Ensuring privacy in training data aggregation for sensitive labels.
method Learning from bag aggregates (LBA) with weighted Gaussian sums, preserving label differential privacy (label-DP).
result Weighted LBA using iid Gaussian weights with randomly sampled disjoint -sized bags provides -label-DP.
This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian upper bounds.
New invariants for RNA foldings and stuck links defined.
problem Defining invariants for RNA foldings and stuck links.
method Assigning Boltzmann weights at classical and stuck crossings.
result Explicit computations of new invariants provided.
A mixture of CNNs improves adult content recognition.
problem Recognizing and restricting inappropriate images like pornography.
method A weighted sum of multiple CNN models trained using OLS.
result The proposed model outperforms single and average models.
Paper proposes DR-NMF for robust NMF with unknown noise model.
problem Robust NMF for unknown noise model.
method Multi-objective NMF with weighted-sum approach, DR-NMF via Frank-Wolfe algorithm.
result DR-NMF is robust to unknown noise model.
Develops algorithms for multi-way similarity clustering in hypergraphs.
problem Challenges of spectral clustering in multi-way similarity settings.
method Hypergraph Spectral Clustering (HSC) and Hypergraph Spectral Clustering with Local Refinement (HSCLR).
result Achieves optimal performance under the weighted stochastic block model.
Paper proposes a new time series prediction method using weighted past data and optimization.
problem Predicting time series data with improved accuracy considering both deterministic and stochastic assumptions.
method The approach uses a weighted sum of past data, solving a constrained linear optimization problem to minimize an outer bound of prediction error.
result The method can outperform existing non-parametric methods in short-term forecasts.
Study symmetry groups and curves from sums of exponentials.
problem Understanding the geometry and symmetry of curves from sums of exponentials.
method Analysis of symmetry groups, winding numbers, and parametrization of the unit circle.
result Unified method for constructing curves with specific properties.
Sum-of-norms clustering recovers mixtures of Gaussians even with infinite samples.
problem Recovering a mixture of Gaussians from a large number of samples.
method Sum-of-norms clustering with equal weights, convex optimization.
result Sum-of-norms clustering can recover mixtures of Gaussians even as the number of samples tends to infinity.
This paper certifies cluster assignments from sum-of-norms clustering algorithms.
problem Certifying the correct cluster assignments from approximate solutions of sum-of-norms clustering.
method Presented a clustering test that identifies and certifies the correct cluster assignment from an approximate solution.
result The correct cluster assignment is guaranteed to be certified by a primal-dual path following algorithm after sufficient iterations.
Weil-Petersson volumes vary continuously with weighted points on a projective line.
problem Continuity of Weil-Petersson volumes in moduli space with weighted points.
method Localization and geometric computation methods.
result CM volume converges to geometric volume as weights approach Calabi-Yau geometry.
We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL dive…
Paper uses SC to estimate hidden interference for WSRM.
problem Maximizing sum-rate with hidden interfering sources.
method Synthetic control (SC) for estimating counterfactual interference in WMMSE.
result SC-WMMSE outperforms original WMMSE in convergence and objective.
Synthesizes methods for estimating treatment effects with multiple controls.
problem Estimating treatment effects with multiple controls and a single treated unit.
method Generalizes synthetic control and difference-in-differences methods to allow negative weights and permanent differences.
result Allows for more flexible and precise estimation of treatment effects.
This work improves graph inference using the degree-4 sum-of-squares hierarchy.
problem Recovering ground-truth binary labelings from corrupted edge observations.
method Apply the degree-4 sum-of-squares hierarchy to a quadratic combinatorial optimization problem.
result The solution of the dual problem is related to edge weights of Johnson and Kneser graphs.
Variance reduced stochastic optimization over directed graphs with row and column stochastic weightsmath.OC
AB-SAGA optimizes distributed optimization over directed graphs using variance reduction and stochastic weights.
problem Optimizing distributed stochastic optimization over directed graphs with stochastic weights.
method AB-SAGA combines variance reduction and network-level gradient tracking, using both row and column stochastic weights.
result AB-SAGA converges linearly to the global optimal with a constant step-size and achieves a linear speed-up over centralized methods.
Optimal approximations of power-laws with exponentialsphysics.data-an
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
The paper introduces new invariants from weighted Betti numbers in triangulated manifolds.
problem Understanding invariants from weighted Betti numbers in triangulated manifolds.
method Introducing a new invariant defined as weighted averages of Betti numbers of induced subcomplexes, and proving its properties under operations on triangulated manifolds.
result The new invariants satisfy Alexander-Dehn-Sommerville type identities and have properties under operations on triangulated manifolds.
Paper identifies neural network weights from few samples using differentiation and tensor products.
problem Identifying weights of shallow neural networks from limited data.
method Uses second-order differentiation and tensor product decomposition to identify weights from a small number of samples.
result Proves successful identification of weight vectors close to orthonormal and constructsively reduces generality.
Develops a new quadrature method for Lebesgue integrals.
problem Finding optimal values and weights for non-Gaussian processes.
method Solves a generalized eigenvalue problem to find value-nodes and weights.
result Advantages in analyzing irregular and stochastic processes.
The paper computes characteristic classes for Lie group representations.
problem Computing characteristic classes for Lie group representations.
method The paper outlines a procedure to compute characteristic classes of irreducible representations of Lie groups, expressing them as polynomial functions in the highest weight.
result The paper expresses characteristic classes of Lie group representations as polynomial functions in the highest weight.
The paper solves numerical integration on graphs by optimizing vertex sampling and weights.
problem Finding efficient sampling and weights for graph functions.
method Rewriting integration as a geometric packing problem and constructing approximate solutions.
result Efficient numerical integration on graphs can be achieved through optimal packing of heat balls.
Summing over 3-manifolds using TQFT partition functions.
problem Summing over all 3-manifolds with fixed boundary.
method Rewriting the sum over 3-manifolds as a sum over homology groups, using TQFT partition functions and topological boundary conditions.
result Existence of a distribution of 2d TQFTs whose ensemble average equals the sum over 3-manifolds.
In this paper, we are interested in constructing general graph-based regularizers for multiple kernel learning (MKL) given a structure which is used to describe the way of combining basis kernels. Such structures are represented by sum-product networks (SPNs) in our method. Accordingly we propose a new convex regulariz…
GP-SUM filters complex non-Gaussian states using Gaussian Processes.
problem Stochastic dynamic filtering and state propagation with complex beliefs.
method GP-SUM combines sampling and probabilistic Bayes filters, using Gaussian Processes for dynamic and observation models.
result GP-SUM outperforms other filters on benchmarks and predicts non-Gaussian states accurately.
Extremal weight projectors generalized for gl(N).
problem Categorify torus skein algebras for gl(N).
method Diagrammatic idempotents in affine extension of Temperley-Lieb category.
result Categorification of power-sum symmetric polynomials.
BGNN improves GNN by modeling interactions between neighbor nodes.
problem Existing GNN models fail to capture interactions between neighbor nodes, leading to suboptimal performance.
method Proposes a new graph convolution operator that augments the weighted sum with pairwise interactions of neighbor nodes.
result Empirical results show BGNN models outperform traditional GNN models in node classification accuracy.
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.
Negative Sasakian manifolds, where the first Chern class of the contact subbundle is a torsion class, can be viewed as Seifert- bundles where the base orbifold has an ample orbifold canonical class. We use this framework to settle completely an open problem formulated by C.Boyer and K.Galicki which asks whether or…
Study evaluates thresholds for removing noise from DNN weights using random matrix theory.
problem Removing noise from deep neural network weights for better approximation.
method Model weights as signal + noise, use random matrix theory to estimate thresholds, evaluate using cosine similarity.
result Proposed threshold estimation method improves approximation quality.
Algorithm minimizes regret and converges to equilibria in Markov games.
problem Regret minimization and convergence to equilibria in general-sum Markov games under adversarial opponents.
method Decentralized algorithm that uses policy optimization and controls path length to achieve sublinear regret.
result Sublinear regret guarantees for convergence to correlated equilibrium in Markov games.
In this paper we study the functional $\SW_{λ_1,λ_2}$, which is the the sum of the Willmore energy, -weighted surface area, and -weighted volume, for surfaces immersed in . This coincides with the Helfrich functional with zero `spontaneous curvature'. Our main result is a complete classification of all …
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
Paper analyzes Min-Sum scheme for solving Laplacian systems and flow problems.
problem Solving systems of linear equations and computing electric flows in graphs.
method Develops a framework to analyze Min-Sum message passing for voltage and flow problems.
result Characterizes error and convergence of Min-Sum algorithm on general and regular graphs.
We consider framed chord diagrams, i.e. chord diagrams with chords of two types. It is well known that chord diagrams modulo 4T-relations admit Hopf algebra structure, where the multiplication is given by any connected sum with respect to the orientation. But in the case of framed chord diagrams a natural way to define…
A method interprets black-box models using an ensemble of gradient boosting machines.
problem Local and global interpretation of black-box models.
method An ensemble of gradient boosting machines (GBMs) to form a generalized additive model.
result Efficiency and properties demonstrated on synthetic and real datasets.