Related papers: Deep $\Pi^0_1$ Classes
In this paper we formulate a probabilistic model for class-specific discriminant subspace learning. The proposed model can naturally incorporate the multi-modal structure of the negative class, which is neglected by existing class-specific…
We investigate what collections of c.e.\ Turing degrees can be realised as the collection of elements of a separating $\Pi^0_1$ class of c.e.\ degree. We show that for every c.e.\ degree $\mathbf{c}$, the collection $\{\mathbf{c},…
In safety-critical classification, the cost of failure is often asymmetric, yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), that cannot distinguish whether a model's ignorance…
Deep learning is the state-of-the-art in fields such as visual object recognition and speech recognition. This learning uses a large number of layers, huge number of units, and connections. Therefore, overfitting is a serious problem. To…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory…
In this paper, we introduce and investigate a class P of continuous and periodic functions on R. The class P is defined so that second-order central differences of a function satisfy some concavity-type estimate. Although this definition…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
A maximum likelihood based model selection of discrete Bayesian networks is considered. The model selection is performed through scoring function $S$, which, for a given network $G$ and $n$-sample $D_n$, is defined to be the maximum…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
Deep neural network classifiers partition input space into high confidence regions for each class. The geometry of these class manifolds (CMs) is widely studied and intimately related to model performance; for example, the margin depends on…
We study zeroth-order optimization where solutions must minimize a cost $d(s)$ while maintaining high probability under a complex generative prior $L(s)$ (e.g., a parameterized model). This reduces to sampling from a target distribution…
We investigate the satisfiability degree of some equations in finite BCK-algebras; that is, given a finite BCK-algebra and an equation in the language of BCK-algebras, what is the probability that elements chosen uniformly randomly with…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
Class-Incremental Learning is a challenging problem in machine learning that aims to extend previously trained neural networks with new classes. This is especially useful if the system is able to classify new objects despite the original…
Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…
Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…
In this paper, we perform deep neural networks for learning $\psi$-weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association,$\cdots$ and the setting considered here…
These lectures on the combinatorics and geometry of 0/1-polytopes are meant as an \emph{introduction} and \emph{invitation}. Rather than heading for an extensive survey on 0/1-polytopes I present some interesting aspects of these objects;…