In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical applications such as autonomous driving. In this work, we put forward a novel geometric-based approach for improving uncertainty estimations in machine learning models. Our approach involves using the geometric distance of the current input from existing training inputs as a signal for estimating uncertainty, and then calibrating this signal using standard post-hoc techniques. We demonstrate that our method leads to more accurate uncertainty estimations than recently proposed approaches through extensive evaluation on a variety of datasets and models. Additionally, we optimize our approach so that it can be implemented on large datasets in near real-time applications, making it suitable for time-sensitive scenarios.

Uncertainty calibration is the process of adapting machine learning models' confidence estimations to be consistent with the actual success probability of the model [Guo et al., Machine learning classifiers are probabilistic in nature, 2017a]. The model's confidence evaluation on its classifications, and thus inevitably involve uncertainty. Predicting i.e., the model's prediction of the success ratio on a the probability of a specific input to be specific input, is an essential aspect of mission-critical machine correct is called uncertainty (or confidence) estimation learning applications as it provides a realistic estimate and is crucial for risk management. Posthoc of the classification's success probability and facilitates informed model calibrations can improve models' uncertainty decisions about the current situation. Even a very estimations without the need for retraining, accurate model may run into an unexpected situation, which and without changing the model.

Embedding undirected graphs in a Euclidean space has many computational benefits. FastMap is an efficient embedding algorithm that facilitates a geometric interpretation of problems posed on undirected graphs. However, Euclidean distances are inherently symmetric and, thus, Euclidean embeddings cannot be used for directed graphs. In this paper, we present FastMap-D, an efficient generalization of FastMap to directed graphs. FastMap-D embeds vertices using a potential field to capture the asymmetry between the pairwise distances in directed graphs. FastMap-D learns a potential function to define the potential field using a machine learning module. In experiments on various kinds of directed graphs, we demonstrate the advantage of FastMap-D over other approaches.

Embedding undirected graphs in a Euclidean space has many computational benefits. FastMap is an efficient embedding algorithm that facilitates a geometric interpretation of problems posed on undirected graphs. However, Euclidean distances are inherently symmetric and, thus, Euclidean embeddings cannot be used for directed graphs. In this paper, we present FastMap-D, an efficient generalization of FastMap to directed graphs. FastMap-D embeds vertices using a potential field to capture the asymmetry between the to-and-fro pairwise distances in directed graphs. FastMap-D learns a potential function to define the potential field using a machine learning module. In experiments on various kinds of directed graphs, we demonstrate the advantage of FastMap-D over other approaches.

The MAPF problem is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses and autonomous vehicles. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers make different assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult to establish appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and support researchers and practitioners by providing a unifying terminology for describing common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.

The 2D Multi-Agent Path Finding (MAPF) problem aims at finding collision-free paths for a number of agents, from a set of start locations to a set of goal positions in a known 2D environment. MAPF has been studied in theoretical computer science, robotics, and artificial intelligence over several decades, due to its importance for robot navigation. It is currently experiencing significant scientific progress due to its relevance in automated warehousing (such as those operated by Amazon) and in other contemporary application areas. In this paper, we demonstrate that many recently developed MAPF algorithms apply more broadly than currently believed in the MAPF research community. In particular, we describe the 3D Pipe Routing (PR) problem, which aims at placing collision-free pipes from given start locations to given goal locations in a known 3D environment. The MAPF and PR problems are similar: a solution to a MAPF instance is a set of blocked cells in x-y-t space, while a solution to the corresponding PR instance is a set of blocked cells in x-y-z space. We show how to use this similarity to apply several recently developed MAPF algorithms to the PR problem, and discuss their performance on abstract PR instances. We also discuss further research necessary to tackle real-world pipe-routing instances of interest to industry today. This opens up a new direction of industrial relevance for the MAPF research community.

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for the multi-agent path-finding problem. However,existing variants of CBS do not use any heuristics that estimate future work. In this paper, we introduce different admissible heuristics for CBS by aggregating cardinal conflicts among agents. In our experiments, CBS with these heuristics outperforms previous state-of-the-art CBS variants by up to a factor of five.

Many real-world combinatorial problems exhibit structure in the way in which their variables interact. Such structure can be exploited in the form of "factors" for representational as well as computational benefits. Factored representations are extensively used in probabilistic reasoning, constraint satisfaction, planning, and decision theory. In this paper, we formulate the factored shortest path problem (FSPP) on a collection of constraints interpreted as factors of a high-dimensional map. We show that the FSPP is not only a generalization of the regular shortest path problem but also particularly relevant to robotics. We develop factored-space heuristics for A* and prove that they are admissible and consistent. We provide experimental results on both random and handcrafted instances as well as on an example robotics domain to show that A* with factored-space heuristics outperforms A* with the Manhattan Distance heuristic in many cases.

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic.

Multi-agent path finding (MAPF) is a well-studied problem in artificial intelligence, where one needs to find collision-free paths for agents with given start and goal locations. In video games, agents of different types often form teams. In this paper, we demonstrate the usefulness of MAPFalgorithms from artificial intelligence for moving such non-homogeneous teams in congested video game environments.