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Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.
Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a…
A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…
We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based…
Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations…
In stochastic analysis, the flow of information through time is typically modelled using a filtration. We introduce some of the basic ideas involving enlargements of filtration. Here, we focus mainly on initial enlargements, where a given…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
Machine learning systems such as large scale recommendation systems or natural language processing systems are usually trained on billions of training points and are associated with hundreds of billions or trillions of parameters. Improving…
It is well known that to give an oplax functor of bicategories $\mathbf{1}\to\mathscr{C}$ is to give a comonad in $\mathscr{C}$. Here we generalize this fact, replacing the terminal bicategory by any bicategory $\mathscr{A}$ for which the…
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…
Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and…
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable…
Probing classifiers have emerged as one of the prominent methodologies for interpreting and analyzing deep neural network models of natural language processing. The basic idea is simple -- a classifier is trained to predict some linguistic…
Recently there has been significant activity in developing algorithms with provable guarantees for topic modeling. In standard topic models, a topic (such as sports, business, or politics) is viewed as a probability distribution $\vec a_i$…
We define the notion of 2-filtered 2-category and give an explicit construction of the bicolimit of a category valued 2-functor. A category considered as a trivial 2-category is 2-filtered if and only if it is a filtered category, and our…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…