A study ranks critical Lean Six Sigma tools for implementation in Portuguese companies.
problem Identifying the most important tools for successful Lean Six Sigma implementation in Portugal.
method An online survey with Portuguese consultants evaluated 37 tools based on frequency of use, difficulty, importance, and impact. A ranking was developed using a procedure to assess consultants' know-how.
result Honshin Kanri, VOC, VSM were identified as the most important tools for Lean Six Sigma implementation.
The problem of ranking is a multi-billion dollar problem. In this paper we present an overview of several production quality ranking systems. We show that due to conflicting goals of employing the most effective machine learning models and responding to users in real time, ranking systems have evolved into a system of …
Study manifolds with positive intermediate Ricci curvature and large symmetry rank.
problem Closed, simply connected manifolds with positive 2nd-intermediate Ricci curvature and large symmetry rank.
method New tools for studying isometric actions on closed manifolds with positive kth-intermediate Ricci curvature, including isotropy rank lemma, symmetry rank bound, and connectedness principle.
result Even dimensional manifolds with large symmetry rank must have trivial odd degree integral cohomology and are either spheres or complex projective spaces.
New tools compute index of symmetry in homogeneous fibrations.
problem Computing the index of symmetry in homogeneous fibrations.
method Developed new tools to compute the index of symmetry.
result Determined the index of symmetry of various homogeneous spaces.
We study information theoretic methods for ranking biomarkers. In clinical trials there are two, closely related, types of biomarkers: predictive and prognostic, and disentangling them is a key challenge. Our first step is to phrase biomarker ranking in terms of optimizing an information theoretic quantity. This formal…
Scorio.jl ranks systems from repeated tasks using various methods.
problem Evaluating and ranking systems from repeated responses to shared tasks.
method Common tensor-based interface for multiple ranking methods.
result Pilot experiments show stability and runtime scaling.
Maximal rank Coxeter quotients found for 1.7M knots up to 16 crossings.
problem Finding maximal rank Coxeter quotients for knots.
method Computational approach to find Coxeter quotients for knots up to 16 crossings.
result Verification of Meridional Rank Conjecture for 595,515 knots.
We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on meridional rank are obtained via Coxeter quotients of the groups of link complement…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…
We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.
Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank-k projection can be preserved using a smaller sketch of the original data matrix. We present a general structural result outlining four sufficient conditions to achieve projection-cost preservation. These condit…
In statistical connectomics, the quantitative study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject. While using the element-wise sampl…
Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding low-rank approximations to Boolean matrices. In this paper we give what is to the best …
We provide an example in each rank of an ageometric fully irreducible outer automorphism whose ideal Whitehead graph has a cut vertex. Consequently, we show that there exist examples in each rank of Handel-Mosher axis bundles that are not just a single axis, as well as of "nongeneric" behavior in the sense of the "trai…
We consider the problem of ranking a set of items from pairwise comparisons in the presence of features associated with the items. Recent works have established that O(nlog(n)) samples are needed to rank well when there is no feature information present. However, this might be sub-optimal in the presence of associat…
In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful novel concept in algebraic geometry that generalizes the tensor CP decomposition…
A JAX toolbox solves optimal transport problems for point clouds and histograms.
problem Optimal transport problems between point clouds and histograms.
method Automatic and custom reverse mode differentiation, vectorization, just-in-time compilation, and accelerators support.
result Solves a wide range of optimal transport problems including regularized OT, barycenters, Gromov-Wasserstein, and low-rank solvers.
New concept of coarse medians for higher rank symmetric spaces.
problem Understanding medians in higher rank symmetric spaces.
method Introducing coarse r-median spaces and proving their existence. result Existence of coarse higher medians on divisible and quasi-homogeneous convex domains.
Researchers show mixtures of ranking models are generally identifiable.
problem Understanding when and how parameters of mixtures of ranking models can be uniquely determined.
method Algebraic geometry framework applied to verify the number of solutions in polynomial systems.
result Popular mixtures of ranking models with two components are generically identifiable.
Develops a method to infer partial rankings from sparse comparisons.
problem Challenges in ranking items with limited and noisy comparisons.
method Nonparametric Bayesian approach for learning partial rankings.
result Finds partial rankings that distinguish meaningful differences only when data supports it.
CRS model improves ranking data modeling with theoretical guarantees.
problem Lack of rich, multimodal models for ranking data.
method Contextual Repeated Selection (CRS) model for multimodal ranking data.
result CRS model significantly outperforms existing methods in various ranking contexts.
We accelerate the power method for strong low-rank approximation using fast sketching.
problem Efficiency bottleneck in power method for large target ranks.
method Developed an algorithmic and theoretical framework for accelerating the power method using fast sketching.
result Simple and provably efficient methods for singular value decomposition, low-rank factorization, and Nyström approximation.
In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is incomplete, which prevents the direct application of existing modelling tools for complet…
The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.
problem Recovering tensors with low symmetric rank from symmetric rank-one measurements.
method Covering numbers argument, Carbery-Wright inequality, orthogonal polynomials, Fano's inequality.
result Near-optimal sample complexity bounds for log-concave distributions.
Paper discusses extending Gini score for tied rankings and case weights.
problem Extending Gini score for tied rankings and case weights.
method Discuss and adapt Gini score for ties and case weights.
result Gini score can be used for tied rankings and case weights.
Rank concepts help explain deep learning's effectiveness.
problem Limited formal understanding of deep learning.
method Introducing rank concepts to explain generalization and expressiveness.
result Gradient-based training induces low rank in neural networks.
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to n⌊p/2⌋ for a p-th order tensor in Rnp. Previously no efficient algorithm can decompose 3rd order ten…
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as LTL, the problem can be cast as looking for a linear map between two …
Batch normalization prevents rank collapse in deep networks, improving training stability.
problem Rank collapse in randomly initialized deep networks with increasing depth.
method Investigates spectral instabilities in random matrices and uses batch normalization to avoid rank collapse.
result Batch normalization prevents rank collapse in both linear and ReLU networks, improving training stability.
Nonnegative low-rank matrix recovery can have spurious local minima.
problem Nonnegative low-rank matrix recovery problems can have spurious local minima.
method Investigated projected gradient methods for nonnegative low-rank recovery problems.
result Benign nonconvexity holds in the fully-observed case with RIP constant δ=0 but fails in the partially-observed case and higher-rank ground truths.
Paper develops new patterns for unique matrix completions.
problem Developing unique completions for non-random matrix patterns.
method Formulated low-rank matrix completion using Plucker coordinates.
result Provides two families of patterns for any rank.
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank dete…
Paper introduces robust methods for consensus ranking in AI systems.
problem Developing reliable ranking systems in AI despite contaminated data.
method Introduces robustness concepts and statistical methods for consensus ranking.
result Proposes extensions of breakdown point for consensus ranking.
Bayesian model ranks treatments in multi-response experiments.
problem Identifying the best treatment among competing ideal properties.
method Bayesian approach with Markov Chain Monte Carlo algorithm.
result Reliable inference of treatment ranks in practice.
Analyzes the structure and rank of neural network Hessians.
problem Understanding redundancy in overparameterized neural networks.
method Theoretical tools to analyze Hessian map range and rank deficiency.
result Exact formulas and tight upper bounds for Hessian rank of deep linear networks.
Paper tackles underranking in group-fair ranking systems, proving a trade-off and presenting an algorithm.
problem Underranking in group-fair ranking systems can worsen social and economic inequalities.
method Formulated underranking as a new problem, proved a lower bound, and presented a fair ranking algorithm.
result Algorithm achieves best of underranking and group fairness, confirming theoretical trade-off.
PILNO uses neural operators to solve PDEs efficiently on point clouds.
problem Solving partial differential equations (PDEs) on point cloud data efficiently.
method Physics-informed low-rank neural operator framework combining low-rank kernel approximations and an encoder-decoder architecture.
result PILNO efficiently approximates solution operators of PDEs on point cloud data, satisfying PDE constraints and boundary conditions.
New methods ensure feature importance rankings are correct with high probability.
problem Stability issues in feature importance scores due to random sampling.
method Hypothesis testing-based techniques to assess and verify the stability of top-ranked features.
result Ensures the most important features are correct with high-probability guarantees.
For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For sy…
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
problem Dimension reduction in robust principal component analysis.
method IRCUR employs CUR decomposition to update the low rank component efficiently.
result IRCUR achieves significant computational efficiency compared to existing algorithms.
We provide a novel proof that the set of directions that admit a saddle connection on a meromorphic quadratic differential with at least one pole of order at least two is closed, which generalizes a result of Bridgeland and Smith, and Gaiotto, Moore, and Neitzke. Secondly, we show that this set has finite Cantor-Bendix…
New framework assesses LLMs' expertise using nonparametric ranking and confidence diagrams.
problem Evaluating and ranking large language models (LLMs) for alignment and performance.
method Nonparametric contextual ranking, confidence diagram, Gaussian multiplier bootstrap.
result Validated confidence diagram for assessing LLMs' domain-specific expertise.
Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.
problem Describing hyperbolic actions of solvable groups with higher rank abelianizations.
method Extends confining subset theory to apply to solvable groups with higher rank abelianizations.
result Complete description of hyperbolic actions of generalized solvable Baumslag-Solitar groups.
We extend the validity of a Gromov's dimension comparison estimate for topological hypersurfaces to sufficiently large classes of rectifiable sets, arising from Sobolev mappings. Our tools are a suitably weak exterior differentiation for pullback differential forms and a new low rank property for Sobolev mappings.
We show that the finiteness length of an S-arithmetic subgroup Γ in a noncommutative isotropic absolutely almost simple group G over a global function field is one less than the sum of the local ranks of G taken over the places in S. This determines the finiteness properties for arithmetic subgroups in isotro…
We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured groupoids and combinatorial cost. As an application we prove the vanishing of the above invariants for Farber sequences of subgroups of righ…
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional structures underlying such data. However, we currently lack a theoretical understanding …
Deep learning improves PV generation quantile forecasting.
problem Accurate probabilistic forecasting of PV generation.
method Developed an encoder-decoder deep learning model for multi-output quantile PV forecasting.
result The model improves forecast quality and computational efficiency.