Comparing apples and oranges through partial orders: An empirical approach

Abstract

In this paper, we try to understand what people mean when they say that two objects are "similar." This is an important question in the area of human-robot interactions, where robots must interpret human movements in order to act in a "similar" manner. Specifically, we assume that we are given a collection of empirically generated pairwise comparisons between a subset of so-called alternatives (members of a given set), which produces a partial order over the set of alternatives. Based on this partial order, an inverse optimization problem is solved, producing a cost associated with each alternative that is consistent with the partial order. This cost is, moreover, assumed to be generative in that it can be used to select the globally best alternative. An experimental study involving the comparison of apples and oranges is presented to highlight the operation of the proposed approach.

Active Ordinal Querying for Tuplewise Similarity Learning

“…In the case of synthetic data, we instead compute a normalized query count corresponding to the number of constituent triplet comparisons defining the relation of each body point to the head in the tuple. This is justified since in practice we decompose tuples in this way when feeding them into the embedding algorithm, and corresponds to the size of a tuple's transitive reduction (a common representation in learning-to-rank literature (Kingston and Egerstedt 2009)).…”

Active Ordinal Querying for Tuplewise Similarity Learning

“…In the case of synthetic data, we instead compute a normalized query count corresponding to the number of constituent triplet comparisons defining the relation of each body point to the head in the tuple. This is justified since in practice we decompose tuples in this way when feeding them into the embedding algorithm, and corresponds to the size of a tuple's transitive reduction (a common representation in learning-to-rank literature [33]). Additional experimental details such as hyperparameter selection are available in the appendix.…”

Time and output warping of control systems: Comparing and imitating motions

“…2 Note that the subscript t is simply part of the function names xt, yt, etc, and is used to distinguish these functions from others to be introduced later.…”

“…In [2], this problem was partially addressed via supervised learning, and very little structure was assumed; the concept of "similarity" was learned from scratch. In this paper, we instead fix a particular definition for similarity a priori: Namely, we treat mimicking as a special optimal tracking problem with additional degrees of freedom.…”