Related papers: How to Learn a Star: Binary Classification with St…
We analyze the detection and classification of singularities of functions $f = \chi_B$, where $B \subset \mathbb{R}^d$ and $d = 2,3$. It will be shown how the set $\partial B$ can be extracted by a continuous shearlet transform associated…
The structure of data organization is widely recognized as having a substantial influence on the efficacy of machine learning algorithms, particularly in binary classification tasks. Our research provides a theoretical framework suggesting…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
This article will devise data-driven, mathematical laws that generate optimal, statistical classification systems which achieve minimum error rates for data distributions with unchanging statistics. Thereby, I will design learning machines…
This paper addresses the task of set prediction using deep learning. This is important because the output of many computer vision tasks, including image tagging and object detection, are naturally expressed as sets of entities rather than…
Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify…
A binary classifier capable of abstaining from making a label prediction has two goals in tension: minimizing errors, and avoiding abstaining unnecessarily often. In this work, we exactly characterize the best achievable tradeoff between…
Many aspects of the geometry of loss functions in deep learning remain mysterious. In this paper, we work toward a better understanding of the geometry of the loss function $L$ of overparameterized feedforward neural networks. In this…
Seismology of single delta Scuti stars has mainly been inhibited by failing to detect many of the theoretically predicted pulsation modes, resulting in difficulties with mode identification. Theoretical and observational advances have,…
We find asymptotically optimal methods of recovery of the integration operator given values of the function at a finite number of points for a class of multivariate functions defined on a bounded star domain that have bounded in $L_p$ norm…
Binary concepts are empirically used by humans to generalize efficiently. And they are based on Bernoulli distribution which is the building block of information. These concepts span both low-level and high-level features such as "large vs…
I present a brief summary of three different types of binary star - astrometric, spectroscopic and eclipsing - and tabulate the properties of these systems that can be determined directly from observations. Eclipsing binary stars are the…
Stellar models of massive single stars are still plagued by major uncertainties. Testing and calibrating against observations is essential for their reliability. For this purpose one preferably uses observed stars that have never…
A supervised learning algorithm searches over a set of functions $A \to B$ parametrised by a space $P$ to find the best approximation to some ideal function $f\colon A \to B$. It does this by taking examples $(a,f(a)) \in A\times B$, and…
We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an…
The objective of deep metric learning (DML) is to learn embeddings that can capture semantic similarity and dissimilarity information among data points. Existing pairwise or tripletwise loss functions used in DML are known to suffer from…
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
Convex potential minimisation is the de facto approach to binary classification. However, Long and Servedio [2010] proved that under symmetric label noise (SLN), minimisation of any convex potential over a linear function class can result…
Strategic classification, i.e. classification under possible strategic manipulations of features, has received a lot of attention from both the machine learning and the game theory community. Most works focus on analysing properties of the…
Cepheids provide approaches to determining binary parameters which are often complementary to those for main sequence massive and intermediate mass stars. Specifically, we are using high resolution imaging, radial velocities, and X-ray…