We discuss theoretical aspects of the product rule for classification problems in supervised machine learning for the case of combining classifiers. We show that (1) the product rule arises from the MAP classifier supposing equivalent priors and conditional independence given a class; (2) under some conditions, the pro…
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48 results for “production rules”
Learning curves theory for hierarchically compositional data with power-law distributed featuresstat.ML
Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
Neural production systems learn visual dynamics by applying rule templates to entities.
problem Modeling interactions among entities in structured visual environments.
method Inspired by production systems, the paper uses rule templates to bind placeholder variables to specific entities, scoring and applying the best fitting rules to update entity properties.
result The architecture achieves robust future-state prediction and extrapolation from simple to complex environments, outperforming GNNs.
Machine learning accelerates Lie algebra computations.
problem Computing tensor products and branching rules of Lie algebras.
method Machine learning for Lie algebra computations.
result Achieves significant speed-ups in Lie algebra computations.
We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui et al (2010) propose "SAFE" rules that guarantee that a coefficient will be zero in the solution, based on the inner products of each predictor with the outcome. In this paper we propose strong …
An analysis is made of reality conditions within the context of noncommutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule is equivalent to the reality condition. We show also that the matrix which determines the reality condition must satisfy the Yang-…
No fair and strategy-proof automated market maker exists for more than two assets.
problem Designing a fair and strategy-proof automated market maker for multiple assets.
method Analyzing the weighted-product family of aggregation rules and their properties.
result No aggregation rule is both fair and strategy-proof for more than two assets.
Study identifies regions where scoring rules reliably detect forecast errors.
problem Insufficient reliability of scoring rules in evaluating multivariate probabilistic forecasts.
method Systematic finite-sample analysis of proper scoring rules on synthetic and real-world data.
result Identified regions of reliability for scoring rules in time-series forecasting.
Backward propagation rules for warped products under Ricci flow.
problem Understanding how warped product structures behave under Ricci flow.
method Establishing sufficient conditions for backward propagation of warped product structures.
result Asymptotically conical shrinkers are multiply-warped products over Einstein manifolds.
Product models of low dimensional experts are a powerful way to avoid the curse of dimensionality. We present the ``under-complete product of experts' (UPoE), where each expert models a one dimensional projection of the data. The UPoE is fully tractable and may be interpreted as a parametric probabilistic model for pro…
We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invariant probability measure. We interpret the probability measure as arising via the Born rule from a translation invariant matrix product state.
We classify 4-dimensional austere submanifolds in Euclidean space ruled by 2-planes. The algebraic possibilities for second fundamental forms of an austere 4-fold M were classified by Bryant, falling into three types which we label A, B, and C. We show that if M is 2-ruled of Type A, then the ruling map from M into the…
PSD models simplify probability density estimation.
problem Effective modeling of probability densities for inference.
method Positive semi-definite (PSD) models for non-negative functions.
result PSD models efficiently support product and sum rules.
Lack of labeled training data is a major bottleneck for neural network based aspect and opinion term extraction on product reviews. To alleviate this problem, we first propose an algorithm to automatically mine extraction rules from existing training examples based on dependency parsing results. The mined rules are the…
We point out that the Homfly polynomial (that is to say, Ocneanu's trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin's braid group. These bear a close connection to the Morton-Franks-Williams inequality. In these structures, the sets of positive, respectively n…
Study on embedding tree products into groups, distinguishing them.
problem Quasi-isometric embedding of tree products into various groups.
method Using coarse embeddings of products of bushy trees into hierarchically hyperbolic spaces.
result Quasi-isometrically distinguish and rule out embeddings between groups.
We describe the cohomology ring of the moduli space of a flexible polygon in geometrically meaningful terms. We propose two presentations, both are computation friendly: there are simple rules for cup product.
The study characterizes constant curvature manifolds using ruled surfaces.
problem Characterizing manifolds of constant curvature using ruled surfaces.
method Investigating ruled surfaces in 3d Riemannian manifolds, finding stiction curve, distribution parameter, and fundamental forms.
result Identifies necessary and sufficient conditions for extrinsically flat surfaces to be ruled and proves manifold properties.
Paper analyzes constant-product market making protocols.
problem Understanding and optimizing constant-product market making.
method Mathematical analysis of trade splitting and fee recompounding.
result Splitting trades does not affect final exchange rate.
SigD2 reduces noisy rules in rule-based classifiers for better accuracy and readability.
problem Redundant and noisy rules in rule-based classifiers reduce model accuracy and readability.
method Two-stage pruning strategy and ensemble methods (bagging and boosting) to reduce noise and improve model performance.
result SigD2 and ACboost ensemble models outperform state-of-the-art classifiers in terms of accuracy and rule count.
Paper proposes efficient cost functions for automated market makers in DeFi.
problem Inefficient and computationally complex cost functions in DeFi.
method Proposes and analyzes constant circle/ellipse based cost functions.
result Proposed cost functions are computationally efficient and robust against attacks.
New tuning rules for Metropolis algorithms derived from Bayesian large-sample asymptotics.
problem Optimal scaling in random-walk Metropolis algorithms under realistic assumptions.
method Large-sample asymptotics to derive weak convergence results and tuning guidelines.
result Tuning guidelines consistent with previous ones when target density is product form, accounting for correlation structure.
We show that for any Legendrian link in the -jet space of the -graded ruling polynomial, , is determined by the Thurston-Bennequin number and the HOMFLY-PT polynomial. Specifically, we recover as a coefficient of a particular specialization of the HOMFLY-PT polynomial. Furthermore, …
New Fourier features improve high-precision approximation in large-scale problems.
problem Designing scalable, high-precision Fourier features for large-scale kernel methods.
method Introducing a new family of quadrature rules that accurately approximate the Gaussian measure in higher dimensions.
result Improved approximation bounds with new Fourier features.
Learning to see through data is central to contemporary forms of algorithmic knowledge production. While often represented as a mechanical application of rules, making algorithms work with data requires a great deal of situated work. This paper examines how the often-divergent demands of mechanization and discretion ma…
We study an economic model where agents trade a variety of products by using one of three competing rules: "need", "greed" and "noise". We find that the optimal strategy for any agent depends on both product composition in the overall market and composition of strategies in the market. In particular, a strategy that do…
This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate transformation rules for integral order forms are also computed. Matrix order f…
Smooth -supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the "scalar product" of the involved -degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degre…
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the …
Detects anomalies in product health metrics at eBay for better alerts.
problem Detecting anomalies in unsupervised product health metrics at eBay.
method Developed a Moving Metric Detector (MMD) for anomaly detection and a point-wise ranking model for alert retrieval.
result Improves alert precision and avoids alert spamming in eBay production.
The study develops a logic reasoner to verify MS case management specifications.
problem Ensuring correctness and solvability of abstract clinical work products.
method Developed a logic reasoner using UML class and state diagrams, SPIN, and ODM.
result Formal representations of UML diagrams proved consistent for MS case management.
Let Sigma be a smooth complex curve, and let S be the product ruled surface Sigma \times CP^1. We prove a correspondence conjectured by Donaldson between finite energy U(2)-instantons over the cylinder Sigma \times S^1 \times R, and rank 2 holomorphic bundles over S whose restrictions to the divisors at infinity are st…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information beyond just values at some inputs, but also effectively constrain the search space. …
We give a simple construction of the Bernstein-Gelfand-Gelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry. This method permits us to define the additional structure of a bilinear differential cup product on this sequence, satisfying a Leibniz rule up to curvature terms.…
Retrosynthesis is one of the fundamental problems in organic chemistry. The task is to identify reactants that can be used to synthesize a specified product molecule. Recently, computer-aided retrosynthesis is finding renewed interest from both chemistry and computer science communities. Most existing approaches rely o…
This work proves MultiKrum is robust in mean estimation with adversaries.
problem Mean estimation in the presence of Byzantine adversaries.
method Introducing κ* and constructing upper and lower bounds on MultiKrum's robustness coefficient.
result MultiKrum is the first provably robust aggregation rule, with robustness coefficient bounds.
The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability d…
Para-associative Algebroidsmath.DG
New algebraic structure for vector bundles with special properties.
problem Developing new algebraic structures for vector bundles.
method Introducing para-associative algebroids and showing local triviality conditions.
result Existence of a differential connection is necessary and sufficient for local triviality.
CoLA automates efficient numerical linear algebra for complex matrix structures.
problem Efficiently solving large-scale linear algebra problems with complex matrix structures.
method Combining linear operator abstraction with compositional dispatch rules.
result Automatic and efficient numerical algorithms for various linear algebra operations.
In this paper, we derive a novel probabilistic model of boosting as a Product of Experts. We re-derive the boosting algorithm as a greedy incremental model selection procedure which ensures that addition of new experts to the ensemble does not decrease the likelihood of the data. These learning rules lead to a generic …
State-of-the-art learning algorithms, such as random forests or neural networks, are often qualified as "black-boxes" because of the high number and complexity of operations involved in their prediction mechanism. This lack of interpretability is a strong limitation for applications involving critical decisions, typica…
Transform ANNs into interpretable decision trees.
problem Lack of interpretability in ANNs.
method Developed two MDT algorithms: EC-DT and Extended C-Net.
result Extended C-Net generates the most compact and effective trees.
Crocheting Mathematicsmath.HO
Crochet creates precise 2D shapes from 1D material.
problem Creating precise 2D shapes from 1D material.
method Using crochet to generate constant flat, spherical, or hyperbolic shapes.
result Crochet is the most flexible and precise method for building dynamical systems with high curvature precision.
It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobás and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describi…
CT compares two distributions using Bayes' theorem and chain rule.
problem Measuring the difference between two probability distributions.
method Conditional transport (CT) using chain rule and Bayes' theorem.
result CT strikes a good balance between mode-covering and mode-seeking behaviors.
The topology of the intersection of two real homogeneous coaxial quadrics was studied by the second author who showed that its intersection with the unit sphere is in most cases diffeomorphic to a connected sum of sphere products. Combining that approach with a recent one (due to Antony Bahri, Martin Bendersky, Fred Co…
In this paper we study a class of insurance products where the policy holder has the option to insure of its annual Operational Risk losses in a horizon of years. This involves a choice of out of years in which to apply the insurance policy coverage by making claims against losses in the given year. The…
A global agreement on how to reduce and cap human footprint, especially their GHG emissions, is very unlikely in near future. At the same time, bilateral agreements would be inefficient because of their neural and balanced nature. Therefore, unilateral actions would have attracted attention as a practical option. Howev…