Boosts SVMs by perturbing kernels to improve classification of imbalanced and small disjuncts.
problem Class imbalance and small disjuncts in datasets.
method Kernel perturbation to diversify SVMs for boosting, identifying disjuncts.
result Proposed method outperforms state-of-the-art methods on various datasets.
New algorithm learns disjunctions faster than previous methods.
problem Learning Boolean disjunctions in the agnostic PAC model.
method Developed an agnostic learner with complexity 2ildeO(n1/3). result First separation between SQ and CSQ models in distribution-free agnostic learning.
DNF-Net tackles tabular data challenges with neural architecture.
problem Handling tabular data efficiently using neural networks.
method DNF-Net uses a neural architecture with inductive bias corresponding to logical Boolean formulas in disjunctive normal form over affine soft-threshold decision terms.
result DNF-Net significantly outperforms fully connected networks on tabular data.
A new algorithm reduces imbalanced data classification errors in multi-class settings.
problem Imbalanced data classification, especially with noise and overlapping classes.
method MC-CCR algorithm combining cleaning and resampling.
result High robustness to noise and superior performance compared to state-of-the-art methods.
Query2box embeds complex queries as boxes to handle logical operations in large KGs.
problem Handling complex logical queries on large-scale incomplete knowledge graphs.
method Embed KG entities and queries into a vector space as boxes, handling conjunctions as intersections and disjunctions through Disjunctive Normal Form.
result Query2box achieves up to 25% relative improvement over state-of-the-art methods.
We obtain multirelative connectivity statements about spaces of smooth embeddings, deducing these from analogous results about spaces of Poincare embeddings that were established in our previous paper.
Study symplectic forms on manifolds to find Lagrangian pinwheels that can be separated.
problem Determine conditions for symplectic forms to carry disjoint Lagrangian pinwheels.
method Use rational blow-up to analyze Lagrangian pinwheels in symplectic manifolds.
result Conditions for disjunction of Lagrangian pinwheels in specific manifolds.
Paper proposes a new method to secure power system operation using machine learning.
problem Ensuring secure power system operation under high uncertainty.
method Embedding disjunctive rules from Decision Trees in an optimization framework using GDP and a two-step search method.
result The method achieves efficient system control at a marginal increase in system price compared to an oracle model.
We obtain multirelative connectivity statements about spaces of Poincare embeddings, as precursors to analogous statements about spaces of smooth embeddings. The latter are the key to convergence results in the functor calculus approach to spaces of embeddings.
New method solves matrix completion problems to certifiable optimality.
problem Certifying optimality in low-rank matrix completion.
method Disjunctive branch-and-bound scheme for convex relaxation.
result Decreases optimality gap by two orders of magnitude.
A new framework improves solving mixed-integer convex problems with binary indicators.
problem Optimizing mixed-integer convex problems with binary indicators controlling continuous variables.
method Coordinate Optimality Reformulation (CORe) framework, incorporating coordinate-wise optimality information.
result CORe reformulations improve branch-and-bound performance, especially in sparse and structured settings.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
problem Understanding how neural networks learn and generalize on Boolean data.
method End-to-end analysis of depth-2 discrete fully connected networks and DNF formulas, using Monte Carlo learning.
result Predictable training dynamics and interpretable features emerge, linking inductive bias and generalization.
One of the objectives of designing feature selection learning algorithms is to obtain classifiers that depend on a small number of attributes and have verifiable future performance guarantees. There are few, if any, approaches that successfully address the two goals simultaneously. Performance guarantees become crucial…
We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our "intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems r…
In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet's lemma of disjunction, we determine the homology of the classifying space of their diffeomorphism …
New undersampling method reduces computational complexity for imbalanced datasets.
problem Data imbalance in machine learning datasets.
method Radial-Based Undersampling (RBO) using mutual class potential.
result Significantly reduced time complexity of the proposed algorithm.
The paper proposes an interpretable off-policy learning algorithm for medical treatments.
problem Lack of interpretable methods for personalized treatment decisions from observational data.
method Hyperbox search approach for interpretable policies in disjunctive normal form.
result The proposed algorithm outperforms state-of-the-art methods in terms of regret and is rated highly interpretable by clinical experts.
Algorithm learns halfspaces robust to Massart noise without distribution knowledge.
problem Learning halfspaces in noisy data with arbitrary marginal distribution.
method Poly-time algorithm for distribution-independent PAC learning.
result Achieves misclassification error of η+ε with poly(d, 1/ε) time complexity.
Paper presents a probabilistic diagnostic model for identifying and treating supervised learning degradation issues.
problem Degradation problems in supervised learning, including class imbalance, overlapping, small-disjuncts, noisy labels, and sparseness.
method Develops a novel probabilistic diagnostic model to identify and treat degradation issues in supervised learning.
result Early and correct diagnosis of degradation issues allows for selecting appropriate remediation treatments and unbiased performance metrics.
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive normal form (OR-of-ANDs). A principled objective function is proposed to trade …
Characterizes a specific homology group for certain graphs.
problem Understanding the first uniformly finite homology group with Z coefficients. method Analyzes uniformly locally finite graphs, characterizes the group for trees and Z2 coefficients, and identifies three phenomena for general graphs. result Necessary conditions for non-vanishing of the group in transitive graphs.
SOAR generates rules for both positive and negative classes in binary classification.
problem Lack of interpretability in machine learning models for binary classification.
method Extends or-of-and classification technique to both positive and negative classes.
result Competitive classification performance with simulated-annealing optimization.
We consider the problem of learning a non-negative linear classifier with a 1-norm of at most k, and a fixed threshold, under the hinge-loss. This problem generalizes the problem of learning a k-monotone disjunction. We prove that we can learn efficiently in this setting, at a rate which is linear in both k and…
A Bayesian Boolean Matrix Factorization for cancer genomics
problem Identifying coordinated feature changes in cancer
method Bayesian Boolean Matrix Factorization
result Captures widespread, near-simultaneous chromosome-number changes
Let n≥2. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n−1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism…
Invariant Causal Set Covering Machines avoid spurious associations.
problem Learning algorithms for rule-based models are vulnerable to spurious associations.
method Building on invariant causal prediction, propose Invariant Causal Set Covering Machines for conjunctions/disjunctions of binary-valued rules.
result The method can identify causal parents of a variable of interest in polynomial time.
Improved algorithm for conditional linear regression with heterogeneous covariances.
problem Identifying a linear predictor for a fraction of data with varying covariances.
method Polynomial time algorithm using Disjunctive Normal Form (DNF) to identify a condition and linear predictor.
result Removed requirement for similar covariances in each condition term, improving algorithm applicability.
Deep RL learns effective job shop scheduling rules from raw features.
problem Designing effective priority dispatching rules for job shop scheduling is challenging.
method End-to-end deep reinforcement learning using Graph Neural Networks.
result Agent learns high-quality dispatching rules from raw features and generalizes well to unseen instances.
For an oriented manifold M whose dimension is less than 4, we use the contractibility of certain complexes associated to its submanifolds to cut M into simpler pieces in order to do local to global arguments. In particular, in these dimensions, we give a different proof of a deep theorem of Thurston in foliation …
Energy-based models can generate complex images by combining simpler concepts.
problem Generating natural images that satisfy complex logical combinations of concepts.
method Energy-based models combine probability distributions of simpler concepts to generate compositions.
result Energy-based models can generate images that satisfy conjunctions, disjunctions, and negations of concepts.
A Boolean algebra formalizes task composition for reinforcement learning.
problem Formalizing task composition for efficient learning and problem-solving.
method Formalized tasks as a Boolean algebra, learning goal-oriented value functions, and composing them to solve new tasks.
result Agents can solve new tasks without additional learning by composing value functions in specific ways.
Study integrates reliability constraints into generation planning models.
problem Challenges in integrating reliability constraints with generation planning models.
method Leverages a weighted oblique decision tree (WODT) technique to embed reliability verification constraints.
result Demonstrates effectiveness in achieving reliable and optimal planning solutions.
Proposes NLRL for enhancing neural networks' interpretability.
problem Deep neural networks lack interpretability for humans.
method Introduces neural logic rule layers (NLRL) to represent arbitrary logic rules.
result NLRL-enhanced neural networks can learn complex logic and arithmetic.
New index measures class imbalance impact on classification performance.
problem Class imbalance affects classifier performance beyond imbalance ratio.
method Theoretical study of Bayes optimal classifier, proposing IBI3 and BI3 measures. result Demonstrates the extent of imbalance impact on classification performance.
Quantum approach models economic decisions with probabilistic and dynamic probabilities.
problem Traditional economic models fail to explain recent financial crises.
method Develops a quantum probabilistic framework for economics.
result Quantum circuits can model cognitive phenomena like preference reversal.
Convex polytope trees expand decision trees with interpretable boundaries.
problem High accuracy often requires many nodes in decision trees, reducing interpretability.
method CPT uses logical disjunction of weighted linear decision-makers, geometrically a convex polytope.
result CPT achieves high accuracy with fewer nodes compared to existing methods.
The paper introduces false discovery rate control for BMF to avoid noisy patterns.
problem No guarantees exist for BMF patterns being real, not just noise.
method Proposes false discovery rate (FDR) to control BMF patterns, proving bounds on FDR.
result Improved BMF algorithms using theoretical FDR bounds for rank selection.
A new method learns interpretable decision rules using submodular optimization.
problem Learning interpretable decision rules from data.
method Submodular optimization approach for selecting rules from a large set.
result The method effectively learns interpretable rule sets from real datasets.
Proposes a new method to better understand complex system interactions.
problem Current methods like Granger causality and transfer entropy fail to capture higher-order interactions.
method Introduces a generalized approach to capture multivariate causal interactions.
result The method can distinguish causal roles in synergetic interactions.
Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.
problem Optimization problems involving rank-one convex functions with support constraints.
method Perspective reformulation techniques to exploit conic structure and establish convex hull results.
result Systematic perspective formulations for convex hull descriptions of sets with nonlinear separable or non-separable objective functions and combinatorial constraints.
New method reduces deep learning complexity on IoT devices.
problem High computational complexity limits deep learning on IoT devices.
method Local quantization region for low-bit data representation.
result Models retain accuracy with reduced computational complexity.
New algorithms for private data synthesis using heuristics.
problem Private data synthesis for complex functions.
method Developed algorithms using non-private oracles and certifiable heuristics.
result Efficient private data synthesis for broad classes of functions.
In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.
Connectedness of small clusters in Riemannian and Finsler manifolds proven.
problem Understanding connectedness of small clusters in Riemannian and Finsler manifolds.
method Proved connectedness and small diameter properties for clusters of small volume in both manifolds.
result Clusters in Riemannian manifolds are connected and have small diameter; in Finsler manifolds, they are at most m connected components of small diameter.
Study fundamental groups of small covers and their injective submanifolds.
problem Topology of small covers and their fundamental groups.
method Explicit presentations of fundamental groups and combinatorial data analysis.
result Characterization of 3D small covers with nonnegative scalar curvature.
Extends small-ball method to broader class without uniform small-ball condition.
problem Obtaining high probability lower bounds on quadratic empirical processes.
method Extends small-ball method to allow broader class without uniform small-ball condition, motivated by tournament learning.
result Obtains high probability, almost-isometric lower bound on quadratic empirical process.
The paper finds hyperbolic small knots in many 3-manifolds.
problem Finding small knots in 3-manifolds.
method Explicit examples of hyperbolic small knots in spherical 3-manifolds.
result Explicit examples of hyperbolic small knots in most spherical 3-manifolds.