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Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
Accurate estimation of spatial gait characteristics is critical to assess motor impairments resulting from neurological or musculoskeletal disease. Currently, however, methodological constraints limit clinical applicability of…
Depth perception is fundamental for robots to understand the surrounding environment. As the view of cognitive neuroscience, visual depth perception methods are divided into three categories, namely binocular, active, and pictorial. The…
Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole…
Data today fuels both the economy and advances in machine learning and AI. All aspects of decision making, at the personal and enterprise level and in governments are increasingly data-driven. In this context, however, there are still some…
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile…
Data Science is a multidisciplinary field that plays a crucial role in extracting valuable insights and knowledge from large and intricate datasets. Within the realm of Data Science, two fundamental components are Information Theory (IT)…
While in a classification or a regression setting a label or a value is assigned to each individual document, in a ranking setting we determine the relevance ordering of the entire input document list. This difference leads to the notion of…
Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the…
Analyzing principal components for multivariate data from its spatial sign covariance matrix (SCM) has been proposed as a computationally simple and robust alternative to normal PCA, but it suffers from poor efficiency properties and is…
In this paper we address three different computer vision tasks using a single basic architecture: depth prediction, surface normal estimation, and semantic labeling. We use a multiscale convolutional network that is able to adapt easily to…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
Halfspace (or Tukey) depth is a fundamental and robust measure of centrality of data points in multivariate datasets. Computing the depth of a point with respect to the uniform distribution on an open convex body in $\mathbb{R}^d$ is a…
Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms \cite{llr},…
In the multivariate regression, also referred to as multi-task learning in machine learning, the goal is to recover a vector-valued function based on noisy observations. The vector-valued function is often assumed to be of low rank.…
Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quantitative description of the amount of fitting performed by a given procedure. But, despite this fundamental role in statistics, its behavior not…
Set similarity join, as well as the corresponding indexing problem set similarity search, are fundamental primitives for managing noisy or uncertain data. For example, these primitives can be used in data cleaning to identify different…
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical…
Ranks estimated from data are uncertain and this poses a challenge in many applications. However, estimated ranks are deterministic functions of estimated parameters, so the uncertainty in the ranks must be determined by the uncertainty in…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…