The paper addresses instability in KL divergence estimation using a neural network discriminator.
problem Unstable estimation of KL divergence due to discriminator complexity.
method Using a Reproducing Kernel Hilbert Space (RKHS) to control discriminator complexity.
result Theoretical bound on error probability of KL estimates based on discriminator complexity in RKHS.
Paper proposes a method to stabilize estimation of KL divergence using a discriminator in RKHS.
problem High variance and instability in estimating KL divergence using neural network discriminators.
method Developed a novel construction of the discriminator in RKHS, controlled its complexity, and proved the consistency of the estimator.
result Reduced variance and stabilized training of KL divergence estimates.
Paper analyzes null space for class-specific discriminant learning.
problem Improving discriminant learning for class-specific problems.
method Null space analysis for Class-Specific Discriminant Analysis (CSDA).
result Proposed solutions outperform standard CSDA methods.
Study infinite Euclidean distance discriminants of algebraic varieties.
problem Understanding the structure of data points with infinitely many critical points in Euclidean distance correspondence.
method Developed computer code to compute discriminants and proved properties of fibers.
result Infinite Euclidean distance discriminants contain all data points with infinitely many critical points for the nearest-point problem.
We prove that the discriminant of a nonsingular space curve of genus g≥2 is stable with respect to the standard action of the special linear group.
DNLL loss improves deep LDA accuracy and consistency.
problem Pathological solutions in unconstrained Deep LDA.
method Introducing Discriminative Negative Log-Likelihood (DNLL) loss.
result Deep LDA trained with DNLL produces clean latent spaces and better calibrated probabilities.
This paper improves HS classification by optimizing a geometry-aware transformation.
problem Lack of proper class discrimination in HS data points.
method Optimal geometry-aware transformation using a nonlinear objective function.
result The proposed method enhances classification accuracy on HS data.
The paper studies 8D manifolds with a specific tensor field called a cubic discriminant.
problem Characterizing and understanding 8D Riemannian manifolds with reduced structure groups.
method Introducing an almost quaternion-Hermitian structure and a cubic discriminant tensor field.
result Only two non-flat, integrable examples of these structures are found: quaternion-Kähler symmetric spaces.
Quantum machine learning model for binary classification.
problem Efficiency in high-dimensional binary classification tasks.
method Quantum-classical hybrid algorithm and quantum computer for inference.
result Quantum discriminator achieves 99% accuracy on Iris dataset.
Optimized GAN discriminator using polyharmonic interpolation.
problem Optimizing the discriminator in GANs with higher-order gradient regularization.
method Polyharmonic interpolation and variational calculus.
result The optimal discriminator is a polyharmonic radial basis function.
IMKPL learns interpretable prototypes for better classification.
problem Efficient trade-offs between interpretability and prediction accuracy in kernel-based data.
method Local discrimination in feature space, condensed class-homogeneous neighborhoods, combined embedding.
result IMKPL achieves better interpretability and discriminative representation.
Proposes a method to optimize class mean preservation in kernel-based feature spaces.
problem Optimizing the selection of kernel subspace for better performance.
method Component analysis method for kernel-based dimensionality reduction that optimally preserves class mean distances.
result Discriminant analysis version of the proposed method provides insights into feature space properties.
Proposes a sparse classifier for discriminative Gaussian Mixture Models.
problem Softmax-based discriminative models assume unimodality, leading to parameter redundancy.
method Sparse Bayesian learning for GMM-based discriminative model, reducing parameters and complexity.
result The SDGM outperforms existing softmax-based discriminative models.
Generative model improves latent space convexity through adversarial training on interpolations.
problem Improving latent space convexity in generative models.
method Adversarial training on latent space interpolations within an AE-GAN architecture.
result Convex latent distribution of generated images, preserving realistic resemblances.
Machine learning identifies boundaries of real solutions in polynomial systems.
problem Locating boundaries in parameter space for real solutions of polynomial systems.
method Supervised machine learning approach using nearest neighbor and deep learning approximations.
result Efficiently approximates the real discriminant locus for multidimensional parameter spaces.
A new algorithm interprets DR dimensions and selects features.
problem Lack of interpretability in DR algorithms.
method I-KDR algorithm that maps data to a lower dimensional space with interpretable dimensions and feature selection.
result I-KDR provides better interpretations and higher discriminative performance.
Discriminative classifier for compositional data using hierarchical mixture of Generalized Dirichlet models.
problem Classifying compositional data, especially in spam detection and color space identification.
method Hierarchical mixture of discriminative Generalized Dirichlet classifiers, using variational approximation for parameter learning.
result First time a variational upper-bound for Generalized Dirichlet mixture is proposed in literature.
End-to-end CCA optimizes both discriminative and latent space projections for multi-view learning.
problem Lack of class label information in CCA for multi-view learning tasks.
method Simultaneously optimizes a CCA-based and a task objective in an end-to-end manner to learn a non-linear CCA projection.
result Significant improvement in cross-view classification, regularization with a second view, and semi-supervised learning.
Structure-preserving GANs learn distributions with group symmetry efficiently.
problem Learning distributions with group symmetry efficiently.
method Developed structure-preserving GANs by reducing the discriminator space and designing structured generators.
result Significantly improved sample fidelity and diversity in small data regimes.
A method classifies image-sets using convex cones based on CNN features.
problem Image-set classification using CNN features.
method Modeling CNN features as convex cones and measuring geometric similarity.
result Enhanced classification through discriminant space maximization of between-class variance.
Discriminators can be good feature extractors despite their task focus.
problem Discriminators' features are often considered useless for downstream tasks.
method Theoretical analysis and feature space examination to understand discriminator's role.
result Discriminator features are robust and can prevent mode collapse, making them useful for transfer learning.
Clustering in high-dimensional spaces is nowadays a recurrent problem in many scientific domains but remains a difficult task from both the clustering accuracy and the result understanding points of view. This paper presents a discriminative latent mixture (DLM) model which fits the data in a latent orthonormal discrim…
Improves GANs by sampling from an energy-based model induced by discriminator scores.
problem Improving the quality of images generated by GANs.
method DDLS (Discriminator Driven Latent Sampling) using the sum of latent prior log-density and discriminator output score.
result Significantly improves Inception Score on CIFAR-10 dataset.
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…
Proposes joint domain alignment and discriminative feature learning for deep domain adaptation.
problem Reduces domain shift and misclassification of target domain samples.
method Instance-based and center-based discriminative feature learning methods.
result Learning discriminative features in shared feature space significantly boosts deep domain adaptation performance.
Proposes GM Score to evaluate GANs considering diversity, disentanglement, and discriminability.
problem Evaluation of GANs for sample quality and diversity.
method Integrates various factors including intra-class and inter-class diversity, disentanglement, and discriminability metrics.
result Demonstrates improved evaluation of GANs on MNIST dataset.
The study classifies points on ruled surfaces in 4-space based on geometric properties.
problem Characterizing points on smooth ruled surfaces in 4-space.
method Contact with transverse planes, binary differential equations, and projective transformations.
result Parabolic points on ruled surfaces in 4-space can be classified as butterfly hyperbolic, parabolic, or elliptic based on the discriminant of a binary differential equation.
New model selects uncorrelated and discriminative features for unsupervised feature selection.
problem Selecting uncorrelated and discriminative features in high-dimensional data.
method Adaptive graph-based generalized regression model with uncorrelated constraint and ℓ2,1-norm regularization. result The model effectively selects uncorrelated and discriminative features, improving clustering performance.
New discriminant analysis using GDS projection improves face recognition.
problem Improving face recognition accuracy with limited data.
method GDS projection onto generalized difference subspace, simplified Fisher criterion, normalization.
result GDS projection and gFDA are equivalent, inheriting FDA's discriminant ability.
DCAE learns compact latent representations for one-class novelty detection.
problem Learning compact latent representations for one-class novelty detection.
method DCAE learns compact and collapse-free latent representations through internal discriminative layers of GANs, reconstructing in-class data finely and exclusively.
result DCAE achieves state-of-the-art performance on novelty and adversarial example detection.
Connected Prym eigenforms found in a specific mathematical space.
problem Understanding the structure of Prym eigenforms in a particular mathematical space.
method Proving the connectedness of Prym eigenform loci and classifying square-tiled surfaces.
result The projection of Prym eigenform loci is a single Teichmüller curve.
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter have been proposed that incorporate linear approximations to nonlinear m…
A new algorithm improves kernel-based sparse coding for better data representation.
problem Lack of consistency between training and test optimization frameworks in K-SRC.
method Confident K-SRC (CKSC) with novel discriminative terms and supervised dictionary learning.
result Improves discriminative performance and recall phase in classification.
Study of twisted Kähler-Einstein metrics on Calabi-Yau spaces with singularities.
problem Understanding the collapsed Gromov-Hausdorff limits of Calabi-Yau spaces.
method Analyzing the geometry of twisted Kähler-Einstein metrics on holomorphic fiber spaces.
result Proving the existence of conical-type singularities in the base of fiber spaces.
In this paper we construct the space of smooth 4-manifolds and find the homotopy model for the connected components of the complement to the discriminant. The discriminant of this space is a singular hypersurface and its generic points correspond to manifolds with isolated Morse singularities. These spaces can be consi…
Proposes TFDF to learn transferable and discriminative features for unsupervised domain adaptation.
problem Difficult to induce supervised classifier without labeled data in unsupervised domain adaptation.
method TFDF optimizes transferability and discriminability by aligning distributions and minimizing class confusion.
result TFDF achieves better performance on real-world datasets compared to existing methods.
A new weighted FDA method improves face recognition accuracy.
problem Equal treatment of all class pairs in FDA leads to suboptimal performance.
method Cosine-weighted and automatically weighted FDA methods are proposed.
result Improved face recognition accuracy through weighted FDA.
NCC is inefficient in higher dimensions, NCDA improves performance.
problem Inefficiency of NCC in higher dimensions.
method Combining NCC with LDA to create NCDA.
result NCDA outperforms NCC and competes with LDA and QDA.
We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse zero-variance discriminant analysis (SZVD), for simultaneously performing linear …
Paper proposes an improved domain adaptation technique using class-based information.
problem Adapting classifiers across domains with labeled source and unlabeled target datasets.
method Adversarial discriminator approach informed by class structure in source dataset.
result State-of-the-art results achieved on benchmark datasets.
New method improves GANs by estimating density ratios in feature space with SP loss.
problem Filtering out unrealistic images from GANs trained with suboptimal discriminators.
method Develops DRE-F-SP method based on Softplus loss for density ratio estimation in feature space, and proposes three subsampling methods.
result Empirically shows substantial improvement over existing methods on synthetic and CIFAR-10 datasets.
Proposes a linear dimension reduction method for high-dimensional classification.
problem High-dimensional classification with unequal covariance matrices.
method Simultaneous variable selection and linear dimension reduction followed by quadratic discriminant analysis.
result The method doesn't require estimating precision matrices and scales linearly with the number of measurements.
Enhances image-to-image translation using adversarial latent space.
problem Image-to-image translation task in computer vision.
method Introduces an adversarial discriminator on the latent representation to enforce similar latent space distributions.
result Significantly outperforms competing approaches on MNIST and USPS domain adaptation tasks.
Paper tackles discrimination in predictions using causal modeling.
problem Mathematical guarantee for non-discrimination in predictions.
method Causal modeling to define discrimination, bounding prediction discrimination probability.
result Discrimination in predictions can still exist even if training data is free of discrimination.
New method studies discriminantal loci of algebraic varieties.
problem Understanding discriminantal loci of algebraic varieties.
method Efficient use of groupoids to describe monodromy.
result New insights into discriminantal loci of hypersurfaces.
The study quantifies and compares aleatoric and epistemic discrimination in ML models.
problem Sources of discrimination in ML models and their impact on performance.
method Quantifying aleatoric and epistemic discrimination using statistical experiments and model accuracy.
result State-of-the-art fairness interventions are effective at removing epistemic discrimination but not aleatoric discrimination in datasets with missing values.
A new neural network reduces high-dimensional time-series data for faster classification.
problem Classifying high-dimensional time-series patterns efficiently.
method Developed a time-series discriminant component network (TSDCN) using TSDCA for dimensionality reduction and classification.
result The TSDCN achieves high-accuracy classification and reduces training time.
Develops interpretable low-dimensional kernels with conic discriminant functions.
problem Improving interpretability in kernel-based classification models.
method Gradually constructs simple feature maps leading to interpretable low-dimensional kernels.
result Obtains high accuracy results without extensive hyperparameter tuning.