Triplet sampling was implemented based on the temporal vicinity of samples. Since the input is sequential, for each sample (called anchor) in the sequence, we consider a small and a large temporal window with predefined fixed widths. These two temporal windows are centered at the timestamp of the anchor. Any sample inside the smaller temporal window can be considered as a positive sample and any sample outside the small window but inside the large window can be considered as a negative sample. The widths of the temporal windows roughly depend on the speed of the observer in the environment.

This work presents a data-driven approach for the indoor localization of an observer on a 2D topological map of the environment. State-of-the-art techniques may yield accurate estimates only when they are tailor-made for a specific data modality like camera-based system that prevents their applicability to broader domains. Here, we establish a modality-agnostic framework (called OT-Isomap) and formulate the localization problem in the context of parametric manifold learning while leveraging optimal transportation. This framework allows jointly learning a lowdimensional embedding as well as correspondences with a topological map. We examine the generalizability of the proposed algorithm by applying it to data from diverse modalities such as image sequences and radio frequency signals. The experimental results demonstrate decimeter-level accuracy for localization using different sensory inputs.

This paper solves three NP-hard routing problems, traveling salesman problem (TSP), prize collecting TSP (PCTSP), and capacitated vehicle routing problem (CVRP). This section provides detailed descriptions of PCTSP and CVRP (for TSP, see section 3). The PCTSP is similar to TSP, while there are differences in that we do not have to visit all the nodes and that the destination is not the first node but the depot node, i.e., a tour is not a cycle. Let N be the number of nodes. The problem instance of PCTSP is s = {(xi,λi,µi)}N+1i=1, where the xi R2 is in 2D euclidean coordinates, λi R is the penalty of unvisited node, and µi R is the prize of visited node. The L(π|s) is the tour length, and λ(π|s) is the total penalty of the unvisited nodes.

Dynabench comprises four dynamic tasks with multiple rounds of datasets that will grow over time. Given that here we have to be able to evaluate a wide variety of models, both in the loop and outside of it, we employ a black box post hoc approach, i.e., one that can be applied post-data collection to existing data, on any uploaded model, without requiring anything other than its predictions. One straightforward way to measure fairness then, is to apply clearly delimited, heuristic perturbations to existing evaluation datasets, and measure whether performance drops. Such an approach is similar to recent works that use grammars to heuristically generate pairs of examples varying in gender [58] and/or race [67] in that they utilize predefined lists of words. However, because we also want to ensure minimal consequences on our classification labels, we adopted an approach that is more targeted than grammars and also preserves the original input data distribution: we replace each word in the input data that has a clear signal about race/ethnicity and/or gender identity with a similar word referring to another group, rerun inference, and measure how many labels flipped (i.e., the difference in microaverage accuracy).