arXiv research

Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of cond…

New CPS model tackles conditional probability shift in machine learning.

The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We argue that this is not a conceptually sound approach and suggest an alternative ba…

A new method for adapting to label shifts using class probability matching.

SJS model predicts label shifts in multinomial datasets.

New framework for learning with class-conditional multi-label noise.

Proposes a method to improve class-conditional conformal prediction for many classes.

We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class $C^k$. The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular …

In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Based on existing literat…

We consider the following conditional linear regression problem: the task is to identify both (i) a $k$-DNF condition $c$ and (ii) a linear rule $f$ such that the probability of $c$ is (approximately) at least some given bound $μ$, and $f$ minimizes the $\ell_p$ loss of predicting the target $z$ in the distribution of …

Paper analyzes risk bounds for in-context learning in multiclass classification.

Study on optimal rates for sequential probability assignment using smoothed analysis.

A method for classifying points with minimal queries using Hermite polynomials.

The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure mu belongs…

New linear algorithms improve wSVMs for multiclass probability estimation.

Deep neural operators learn complex probabilistic models efficiently.

New method uses graph generative models for graph classification.

We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic se…

Gradient flows on distributions of distributions for machine learning tasks.

ECBMs unify concept-based interpretations in deep learning models.

A new method calculates optimal decisions from classifier outputs, improving predictions in drug discovery.

Improved multi-class AdaBoost algorithm with stronger weak learnability condition.

We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require a priori knowledge of the number of classes or the relationships between classes. Th…

New tractable density models from squaring neural networks.

We extend Bayes' theorem for upper probabilities considering likelihood uncertainty.

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for in…

Proposes novel wSVMs for sparse learning and accurate probability estimation.

We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an algorithm whose regret with respect to any policy in a comparison class grows as t…

We derive the fast convergence rates of a deep neural network (DNN) classifier with the rectified linear unit (ReLU) activation function learned using the hinge loss. We consider three cases for a true model: (1) a smooth decision boundary, (2) smooth conditional class probability, and (3) the margin condition (i.e., t…

We present a simple generative framework for learning to predict previously unseen classes, based on estimating class-attribute-gated class-conditional distributions. We model each class-conditional distribution as an exponential family distribution and the parameters of the distribution of each seen/unseen class are d…

Kandinsky conformal prediction expands conditional coverage guarantees.

This work introduces a new metric for comparing imprecise probability models.

KCal calibrates deep networks by embedding logits in a metric space.

We characterize the class of exchangeable feature allocations assigning probability $V_{n,k}\prod_{l=1}^{k}W_{m_{l}}U_{n-m_{l}}$ to a feature allocation of $n$ individuals, displaying $k$ features with counts $(m_{1},\ldots,m_{k})$ for these features. Each element of this class is parametrized by a countable matrix $V$…

The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a uniform small-ball estimate: that $Pr(|f| \geq κ\|f\|_{L_2}) \geq δ$ for given const…

This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…

Study of focal-entropy for class-imbalanced classification.

The paper extends optimal transport for linear separability of sheared distributions in supervised learning.

The paper analyzes Tikhonov regularization in Hilbert scales for statistical inverse problems.

We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generali…

We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results f…

A-GPS learns to generate Pareto sets efficiently with user preferences.

We present a framework and analysis of consistent binary classification for complex and non-decomposable performance metrics such as the F-measure and the Jaccard measure. The proposed framework is general, as it applies to both batch and online learning, and to both linear and non-linear models. Our work follows recen…

Develops hypothesis tests for conditional distributions using learning-theoretic bounds.

Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH processes that the invariant distribution is regularly varying. In order to accou…

Establishes upper bounds on generalization error in active learning.

New learning rates derived for Tikhonov-regularized problems without kernel assumptions.

Unified tractability conditions for various compositional inference queries.