Related papers: Learning the Hypotheses Space from data: Learning …

Robust learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While probably approximately correct (PAC) Semantics…

This thesis addresses the challenge of understanding Neural Networks through the lens of their most fundamental component: the weights, which encapsulate the learned information and determine the model behavior. At the core of this thesis…

As an intrinsic and fundamental property of big data, data heterogeneity exists in a variety of real-world applications, such as precision medicine, autonomous driving, financial applications, etc. For machine learning algorithms, the…

Machine learning is the dominant approach to artificial intelligence, through which computers learn from data and experience. In the framework of supervised learning, a necessity for a computer to learn from data accurately and efficiently…

In many, if not most, machine learning applications the training data is naturally heterogeneous (e.g. federated learning, adversarial attacks and domain adaptation in neural net training). Data heterogeneity is identified as one of the…

In this paper, we analyze deep learning from a mathematical point of view and derive several novel results. The results are based on intriguing mathematical properties of high dimensional spaces. We first look at perturbation based…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

A fundamental result of statistical learnig theory states that a concept class is PAC learnable if and only if it is a uniform Glivenko-Cantelli class if and only if the VC dimension of the class is finite. However, the theorem is only…

Following the wide-spread adoption of machine learning models in real-world applications, the phenomenon of performativity, i.e. model-dependent shifts in the test distribution, becomes increasingly prevalent. Unfortunately, since models…

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…

Parameterized systems of polynomial equations arise in many applications in science and engineering with the real solutions describing, for example, equilibria of a dynamical system, linkages satisfying design constraints, and scene…

We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space. Learning is achieved by minimizing the 'penalized Busemann loss', a new…

Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…

Meta learning automatically infers an inductive bias, that includes the hyperparameter of the base-learning algorithm, by observing data from a finite number of related tasks. This paper studies PAC-Bayes bounds on meta generalization gap.…

Existing unsupervised hash learning is a kind of attribute-centered calculation. It may not accurately preserve the similarity between data. This leads to low down the performance of hash function learning. In this paper, a hash algorithm…

Learning curves are a measure for how the performance of machine learning models improves given a certain volume of training data. Over a wide variety of applications and models it was observed that learning curves follow -- to a large…

In this paper, we present some theoretical work to explain why simple gradient descent methods are so successful in solving non-convex optimization problems in learning large-scale neural networks (NN). After introducing a mathematical tool…

While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the…

Statistical learning theory and the Probably Approximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to analyze learning problems and algorithms, and have been studied thoroughly.…

Learning sentence vectors from an unlabeled corpus has attracted attention because such vectors can represent sentences in a lower dimensional and continuous space. Simple heuristics using pre-trained word vectors are widely applied to…