Related papers: Dynamic Products of Ranks
The notion of `stable rank' of a matrix is central to the analysis of randomized matrix algorithms, covariance estimation, deep neural networks, and recommender systems. We compare the properties of the stable rank and intrinsic dimension…
In this paper we describe a dynamic external memory data structure that supports range reporting queries in three dimensions in $O(\log_B^2 N + \frac{k}{B})$ I/O operations, where $k$ is the number of points in the answer and $B$ is the…
Object ranking is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects, which are typically represented as feature vectors, the goal is to learn a ranking…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
In this paper we describe a dynamic data structure that answers one-dimensional stabbing-max queries in optimal $O(\log n/\log\log n)$ time. Our data structure uses linear space and supports insertions and deletions in $O(\log n)$ and…
The sorting operation is one of the most commonly used building blocks in computer programming. In machine learning, it is often used for robust statistics. However, seen as a function, it is piecewise linear and as a result includes many…
We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective…
We explore the connection between an agent's decision problem and her ranking of information structures. We find that a finite amount of ordinal data on the agent's ranking of experiments is enough to identify her (finite) set of…
This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised…
We introduce a dynamic data structure for the compact representation of binary relations $\mathcal{R} \subseteq A \times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of…
In this paper we present several novel efficient techniques and multidimensional data structures which can improve the decision making process in many domains. We consider online range aggregation, range selection and range weighted median…
Stochastic orders are very useful tool to compare the lifetimes of two coherent systems. We show that, under certain conditions, a coherent system of used components performs better (worse) than a used coherent system with respect to…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…
We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…
Rankings are the primary interface through which many online platforms match users to items (e.g. news, products, music, video). In these two-sided markets, not only the users draw utility from the rankings, but the rankings also determine…
We present new results on a number of fundamental problems about dynamic geometric data structures: 1. We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or…
Classic market design theory is rooted in static models where all participants trade simultaneously. In contrast, modern platform-mediated digital markets are fundamentally dynamic, defined by the asynchronous and stochastic arrival of…