The paper shows how data and algorithm interactions affect overparameterized linear regression generalization.
problem Understanding generalization in overparameterized linear regression.
method Introducing data-algorithm compatibility and performing data-dependent trajectory analysis with gradient descent.
result Early stopping iterates lead to better generalization than last-iterate analysis, with weaker restrictions.
Random forest (RF) missing data algorithms are an attractive approach for dealing with missing data. They have the desirable properties of being able to handle mixed types of missing data, they are adaptive to interactions and nonlinearity, and they have the potential to scale to big data settings. Currently there are …
Next generation of embedded Information and Communication Technology (ICT) systems are collaborative systems able to perform autonomous tasks. The remarkable expansion of the embedded ICT market, together with the rise and breakthroughs of Artificial Intelligence (AI), have put the focus on the Edge as it stands as one…
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary approximation techniques like first-order methods and randomization for scalability, a…
Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and generative adversarial networks (GANs), are often developed independently. In this pape…
Notions of compatible and almost compatible pseudo-Riemannian metrics, which are motivated by the theory of compatible (local and nonlocal) Poisson structures of hydrodynamic type and generalize the notion of flat pencil of metrics, are introduced and studied.
The paper tackles entry prediction in row/column-exchangeable matrices with arbitrary missing data.
problem Prediction in matrices with arbitrary missing data.
method Proposes two practical algorithms: one for fast emulation and another for acceleration using algorithmic stability.
result Demonstrates superior performance in synthetic and real-world data sets.
Defines compatibility between Jacobi structures and pseudo-Riemannian metrics on Jacobi algebroids.
problem Generalizing compatibility between Poisson and pseudo-Riemannian metrics to Jacobi structures.
method Introduces and studies compatibility conditions for Jacobi structures and pseudo-Riemannian metrics on Jacobi algebroids.
result Compatibility conditions are preserved under Poissonization and equivalent to Sasakian structures for contact pseudo-metrics.
The paper characterizes compatible linear connections on 3D Finsler manifolds.
problem Characterizing compatible linear connections on Finsler manifolds of dimension three.
method Intrinsic method to characterize compatible linear connections, focusing on indicatrices and Euclidean symmetries.
result If a compatible linear connection is not unique, indicatrices must be Euclidean surfaces of revolution.
The paper proposes reusable network components by making them compatible across tasks.
problem Training networks for different tasks independently leads to incompatible components.
method The paper splits a network into a features extractor and a target task head, and proposes various approaches to make them compatible.
result The proposed methods produce components that are directly compatible without compromising accuracy on original tasks.
Proves compatibility of light cones and projective structures.
problem Clarifying different concepts of compatibility between conformal and projective structures.
method Analyzes compatibility criteria introduced by Ehlers-Pirani-Schild and Trautman-Scholz.
result Proves that the compatibility criterion introduced by Ehlers-Pirani-Schild is correct.
The paper investigates compatible linear connections on Randers spaces and finds a unique extremal connection.
problem Investigating compatible linear connections on Randers spaces.
method Transformed compatibility equations by taking torsion components as variables and determined when these equations have solutions.
result Characterized Randers spaces as non-Riemannian generalized Berwald spaces with a positive constant norm of perturbing term.
The paper studies properties of group relations induced by compatible coarse structures.
problem Properties of asymptotic resemblance relations on groups.
method Generalization of asymptotic dimension and introduction of set theoretic coupling.
result Groups with compatible coarse structures that admit a set theoretic coupling are asymptotic equivalent.
Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity of the new "Codazzi deviation …
Study integrates deep learning with financial data for improved trading strategies.
problem Enhancing predictive performance in algorithmic trading and portfolio optimization.
method Developed embedding techniques to treat limit order book snapshots as image-based input channels.
result Achieved state-of-the-art performance in high-frequency trading algorithms.
The causal compatibility question asks whether a given causal structure graph -- possibly involving latent variables -- constitutes a genuinely plausible causal explanation for a given probability distribution over the graph's observed variables. Algorithms predicated on merely necessary constraints for causal compatib…
Compatibility equations adapted to magnetic geometry.
problem No specific problem stated; magnetic geometry is the setting.
method Established compatibility equations in magnetic geometry.
result Analogues of Gauss, Ricci, and Codazzi-Mainardi equations in magnetic geometry.
Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additi…
New methods reveal compatible liquid crystal phases in 3D.
problem Understanding compatible director fields in 3D liquid crystals.
method Re-derived compatibility conditions using vector calculus.
result Characterized a wide range of compatible liquid crystal phases.
We disprove the generalized Chern-Hamilton conjecture on the existence of critical compatible metrics on contact 3-manifolds. More precisely, we show that a contact 3-manifold (M,α) admits a critical compatible metric for the Chern-Hamilton energy functional if and only if it is Sasakian or its associated Reeb fl…
Some general properties of compatible Poisson brackets of hydrodynamic type are discussed, in particular: (1) an invariant differential-geometric criterion of the compatibility based on the Nijenhuis tensor; (2) the Lax pair with a spectral parameter governing compatible Poisson brackets in the diagonalizable case; (3)…
The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular compatibility conditions. This paper analyzes these compatibilitie…
We show that well known structures on Lie algebroids can be viewed as Nijenhuis tensors or pairs of compatible tensors on Courant algebroids. We study compatibility and construct hierarchies of these structures.
New proof for unique semi-symmetric compatible linear connection on Finsler manifolds.
problem Existence and uniqueness of semi-symmetric compatible linear connections on Finsler manifolds.
method New linear algebra proof without integration, using convex body properties and intrinsic equations.
result Uniqueness of semi-symmetric compatible linear connection proved.
New method improves compatibility of risk stratification models without sacrificing accuracy.
problem Compatibility issues arise when updating clinical machine learning models.
method Proposes rank-based compatibility measure and new loss function.
result Increased compatibility of models by 0.019 with no loss in discriminative performance.
Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor bij is named `compatible' with the curvature tensor if bimKjklm+bjmKkilm+bkmKijlm=0. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetriz…
New method for identifying causal relationships in financial time series data.
problem Identifying causal relationships in nonstationary financial time series data.
method Refined constraint-based causal discovery algorithm (CD-NOTS) for nonstationary time series data.
result CD-NOTS effectively identifies causal connections in financial applications.
The study examines backward compatibility issues in ML systems, especially with noisy data.
problem Backward compatibility challenges in ML systems, especially with noisy data.
method Empirical analysis of ML systems across different architectures and datasets, focusing on data shifts and noise.
result Backward compatibility issues arise even without data shift due to optimization stochasticity and training on large-scale noisy datasets can significantly decrease compatibility.
Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry conditions with respect to vertical and horizontal Christoffel symbols are impose…
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization, and machine learning. Density Estimation is widely adopted in the domain of unsup…
We will introduce two notions of compatibility bettwen pseudo-Riemannian metric and Poisson structure using the notion of contravariant connection introduced by Fernandes R. L., we will study some proprities of manifold endowed with such compatible structures an we will give some examples.
AI systems are being deployed to support human decision making in high-stakes domains. In many cases, the human and AI form a team, in which the human makes decisions after reviewing the AI's inferences. A successful partnership requires that the human develops insights into the performance of the AI system, including …
The nonlinear equations for the general nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived and the integrability of these equations by the method of inverse scattering problem is proved. For these equations, the Lax pairs with a spectral parameter are presented. Moreover, we demo…
Researchers create compatibility complexes for Einstein metrics.
problem Constructing solutions to the conformal-to-Einstein operator.
method Using a method that leverages symmetries and geometric properties.
result At most one independent solution exists under genericity assumptions.
In this Note, we will characterize the Poisson structures compatible with the canonical metric of $\reel^3$. We will also give some relvant examples of such structures. The notion of compatibility used in this Note was introduced and studied by the author in previous papers.
Study star products on Poisson manifolds compatible with reduction.
problem Finding star products compatible with coisotropic reduction.
method Compute second constraint Hochschild cohomology of constraint algebra.
result Determine infinitesimal star products on Poisson manifolds.
In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solv…
XRM discovers environments without human annotations for OOD methods.
problem Costly and biased manual annotations limit OOD methods.
method XRM trains twin networks to mimic mistakes, eliminating hyper-parameters.
result XRM achieves oracle worst-group-accuracy for OOD methods.
Breiman's data analysis dichotomy is outdated, offering a third approach: mechanistic models.
problem Data analysis dichotomy between data modelers and algorithmic modelers.
method Interpolating between simple interpretable models and flexible function approximations using mechanistic models.
result Flexible, interpretable, and scientifically-informed hybrids can provide accurate and robust predictions.
Paper proposes a perfect-fit model for CDO tranches.
problem Achieving a perfect fit to market prices across all CDO tranches.
method Introduces compatibility levels, derives conditions, constructs copula models.
result Demonstrates efficient verification and construction of perfect-fit models.
Four-dimensional, oriented Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are…
No-regret learning with strategic experts, incentivized.
problem Online learning with strategic experts who misreport beliefs.
method Building on wagering mechanisms, we provide algorithms for no-regret and incentive compatibility in both full and partial information settings.
result Our algorithms achieve no regret and incentive compatibility for myopic experts, with comparable regret to classic no-regret algorithms and diminishing regret for forward-looking agents.
BC-Aligner maintains backward compatibility of embeddings after frequent updates.
problem Updating embeddings without requiring consumer teams to retrain their models.
method Learning backward compatible embeddings through BC-Aligner.
result BC-Aligner maintains backward compatibility with existing unintended tasks after multiple model version updates.
We solve the problem of reducing to the simplest and convenient for our purposes, canonical form for an arbitrary pair of compatible nonlocal Poisson brackets of hydrodynamic type generated by metrics of constant Riemannian curvature in order to get an effective construction of the integrable hierarchies related to all…
New contact structures on spheres and tori with weakly compatible metrics.
problem Contact sphere theorem does not hold for weakly compatible metrics.
method Construction of nonvanishing curl eigenfields using Jacobi or trigonometric polynomials.
result Geometric rigidity for tight contact structures on the 3-sphere.
The notion of Poisson manifold with compatible pseudo-metric was introduced by the author in [1]. In this paper, we introduce a new class of Lie algebras which we call a pseudo-Rieamannian Lie algebras. The two notions are strongly related: we prove that a linear Poisson structure on the dual of a Lie algebra has a com…
Let A be a positive injective operator in a Hilbert space (\h, <,>), and denote by [,] the inner product defined by A: [f,g]=<Af,g>. A closed subspace $\s \subset \h$ is called A-compatible if there exists a closed complement for $\s$, which is orthogonal to $\s$ with respect to the inner product [,]. Equivalently, i…
Most policy search algorithms require thousands of training episodes to find an effective policy, which is often infeasible with a physical robot. This survey article focuses on the extreme other end of the spectrum: how can a robot adapt with only a handful of trials (a dozen) and a few minutes? By analogy with the wo…