arXiv research

We study Bayesian discriminative inference given a model family $p(c,\x, θ)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and Bayesian regression, where the margin $p(\x,θ)$ is known to be uninformative about $p(c|\x,…

Lower-dimensional video discriminators improve GAN performance.

EFDA extends LDA to non-Gaussian models using exponential families.

Generative Adversarial Networks (GANs) were intuitively and attractively explained under the perspective of game theory, wherein two involving parties are a discriminator and a generator. In this game, the task of the discriminator is to discriminate the real and generated (i.e., fake) data, whilst the task of the gene…

We present a new, far simpler family of counter-examples to Kushnirenko's Conjecture. Along the way, we illustrate a computer-assisted approach to finding sparse polynomial systems with maximally many real roots, thus shedding light on the nature of optimal upper bounds in real fewnomial theory. We use a powerful recen…

Pairwise discriminators stabilize adversarial training by ensuring the generator's alignment is preserved.

The paper examines Nash equilibrium in GANs for stationary Gaussian processes.

The pattern theory of Grenander is a mathematical framework where patterns are represented by probability models on random variables of algebraic structures. In this paper, we review three families of probability models, namely, the discriminative models, the descriptive models, and the generative models. A discriminat…

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…

Hidden Markov Chains and Linear-chain CRFs are equivalent.

We exploit techniques from classical (real and complex) algebraic geometry for the study of the standard twistor fibration $π:\mathbb{CP}^{3}\to S^{4}$. We prove three results about the topology of the twistor discriminant locus of an algebraic surface in $\mathbb{CP}^{3}$. First of all we prove that, with the exceptio…

Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the unknown distribution of a given data set by optimizing an objective function through a…

Generative adversarial networks (GAN) approximate a target data distribution by jointly optimizing an objective function through a "two-player game" between a generator and a discriminator. Despite their empirical success, however, two very basic questions on how well they can approximate the target distribution remain…

New principle controls graph-informed adversarial discrepancies.

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…

New framework assesses neural sensitivity to small perturbations.

Incorporating feature selection into a classification or regression method often carries a number of advantages. In this paper we formalize feature selection specifically from a discriminative perspective of improving classification/regression accuracy. The feature selection method is developed as an extension to the r…

A new probabilistic model for semi-supervised learning unifies various methods.

In this paper, we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the discriminative function space commonly suffer from the problem that the gradient produced by …

Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for learning implicit models are generative adversarial networks (GANs) which learn pa…

While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent works have shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al. suggests a dilemma about GANs' statistical properties: powerful d…

Threshold tests have recently been proposed as a useful method for detecting bias in lending, hiring, and policing decisions. For example, in the case of credit extensions, these tests aim to estimate the bar for granting loans to white and minority applicants, with a higher inferred threshold for minorities indicative…

The paper studies vector bundles over surfaces, focusing on singularity formation.

In this paper, we investigate the underlying factor that leads to failure and success in the training of GANs. We study the property of the optimal discriminative function and show that in many GANs, the gradient from the optimal discriminative function is not reliable, which turns out to be the fundamental cause of fa…

Random Forests are reinterpreted as generative models to handle missing data and detect outliers.

$KS$-algebra consists of expressions constructed with four kinds operations, the minimum, maximum, difference and additively homogeneous generalized means. Five families of $Z$-classifiers are investigated on binary classification tasks between English phonemes. It is shown that the classifiers are able to reflect well…

Paper proposes Roweisposes for 3D action recognition using generalized eigenvalue problem.

A new IPM uses ReLU networks to measure probability discrepancies.

A new method generalizing subspace learning for improved classification.

Study shows infinite kernels in topological monodromy for curve families.

A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this framework and its convergence proven using the Expectation-Maximization algorithm. …

A basic question in learning theory is to identify if two distributions are identical when we have access only to examples sampled from the distributions. This basic task is considered, for example, in the context of Generative Adversarial Networks (GANs), where a discriminator is trained to distinguish between a real-…

We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …

Researchers use information geometry to analyze and improve DRWs for node classification.

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Lege…

We present a framework to understand GAN training as alternating density ratio estimation and approximate divergence minimization. This provides an interpretation for the mismatched GAN generator and discriminator objectives often used in practice, and explains the problem of poor sample diversity. We also derive a fam…

We identify two issues with the family of algorithms based on the Adversarial Imitation Learning framework. The first problem is implicit bias present in the reward functions used in these algorithms. While these biases might work well for some environments, they can also lead to sub-optimal behavior in others. Secondl…

We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or t…

Study bifurcations of curves on surfaces in Minkowski 3-space.

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state…

For each discriminant $D>1$, McMullen constructed the Prym-Teichmüller curves $W_D(4)$ and $W_D(6)$ in $\mathcal{M}_{3}$ and $\mathcal{M}_{4}$, which constitute one of the few known infinite families of geometrically primitive Teichmüller curves. In the present paper, we determine for each $D$ the number and type of or…

New LFR algorithm ensures fair predictions with theoretical guarantees.

The study quantifies and compares aleatoric and epistemic discrimination in ML models.

Prym-Teichmüller curves $W_D(4)$ constitute the main examples of known primitive Teichmüller curves in the moduli space $\mathcal{M}_3$. We determine, for each non-square discriminant $D>1$, the number and type of orbifold points in $W_D(4)$. These results, together with the formulas of Lanneau-Nguyen and Möller for th…

Generative model explains self-supervised learning across various tasks.

Discrimination-aware classification is receiving an increasing attention in data science fields. The pre-process methods for constructing a discrimination-free classifier first remove discrimination from the training data, and then learn the classifier from the cleaned data. However, they lack a theoretical guarantee f…

Discriminator guidance improves autoregressive diffusion models for generating molecular graphs.

Solves GAN mode collapse by assigning minibatches to multiple discriminators.