We present experimental and theoretical results on a method that applies a numerical solver iteratively to solve several non-negative quadratic programming problems in geometric optimization. The method gains efficiency by exploiting the potential sparsity of the intermediate solutions. We implemented the method to call quadprog of MATLAB iteratively. In comparison with a single call of quadprog, we obtain a 10-fold speedup on two proximity graph problems in $\mathbb{R}^d$ on some public data sets, a 10-fold speedup on the minimum enclosing ball problem on random points in a unit cube in $\mathbb{R}^d$, and a 5-fold speedup on the polytope distance problem on random points from a cube in $\mathbb{R}^d$ when the input size is significantly larger than the dimension; we also obtain a 2-fold or more speedup on deblurring some gray-scale space and thermal images via non-negative least square. We compare with two minimum enclosing ball software by G\"{a}rtner and Fischer et al.; for 1000 nearly cospherical points or random points in a unit cube, the iterative method overtakes the software by G\"{a}rtner at 20 dimensions and the software by Fischer et al. at 170 dimensions. In the image deblurring experiments, the iterative method compares favorably with other software that can solve non-negative least square, including FISTA with backtracking, SBB, FNNLS, and lsqnonneg of MATLAB. We analyze theoretically the number of iterations taken by the iterative scheme to reduce the gap between the current solution value and the optimum by a factor $e$. Under certain assumptions, we prove a bound proportional to the square root of the number of variables.
相關內容
We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are special cases of coalgebraic invariants on mixed-variance functors. We then introduce the notion of a locally maximal logical refinement of a given predicate, with a view to enabling inductive reasoning, and identify sufficient conditions on the overall setup in which locally maximal logical refinements canonically exist. Finally, we develop induction-up-to techniques that simplify inductive proofs via logical predicates on systems encoded as (certain classes of) higher-order GSOS laws by identifying and abstracting away from their boiler-plate part.
Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these methods often converge to locally optimal solutions and frequently switch between different local minima, leading to inefficient and unsafe robot motion. In this work, We propose a novel topology-driven trajectory optimization strategy for dynamic environments that plans multiple distinct evasive trajectories to enhance the robot's behavior and efficiency. A global planner iteratively generates trajectories in distinct homotopy classes. These trajectories are then optimized by local planners working in parallel. While each planner shares the same navigation objectives, they are locally constrained to a specific homotopy class, meaning each local planner attempts a different evasive maneuver. The robot then executes the feasible trajectory with the lowest cost in a receding horizon manner. We demonstrate, on a mobile robot navigating among pedestrians, that our approach leads to faster and safer trajectories than existing planners.
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems -- including matrix-vector product, matrix inversion, matrix multiplication and powering -- existing classical time-space tradeoffs, several of which are tight for every space bound, also apply to quantum algorithms. For example, for almost all matrices $A$, including the discrete Fourier transform (DFT) matrix, we prove that quantum circuits with at most $T$ input queries and $S$ qubits of memory require $T=\Omega(n^2/S)$ to compute matrix-vector product $Ax$ for $x \in \{0,1\}^n$. We similarly prove that matrix multiplication for $n\times n$ binary matrices requires $T=\Omega(n^3 / \sqrt{S})$. Because many of our lower bounds match deterministic algorithms with the same time and space complexity, we show that quantum computers cannot provide any asymptotic advantage for these problems with any space bound. We obtain matching lower bounds for the stronger notion of quantum cumulative memory complexity -- the sum of the space per layer of a circuit. We also consider Boolean (i.e. AND-OR) matrix multiplication and matrix-vector products, improving the previous quantum time-space tradeoff lower bounds for $n\times n$ Boolean matrix multiplication to $T=\Omega(n^{2.5}/S^{1/3})$ from $T=\Omega(n^{2.5}/S^{1/2})$. Our improved lower bound for Boolean matrix multiplication is based on a new coloring argument that extracts more from the strong direct product theorem used in prior work. Our tight lower bounds for linear algebra problems require adding a new bucketing method to the recording-query technique of Zhandry that lets us apply classical arguments to upper bound the success probability of quantum circuits.
Pyramidal clustering method generalizes hierarchies by allowing non-disjoint classes at a given level instead of a partition. Moreover, the clusters of the pyramid are intervals of a total order on the set being clustered. [Diday 1984], [Bertrand, Diday 1990] and [Mfoumoune 1998] proposed algorithms to build a pyramid starting with an arbitrary order of the individual. In this paper we present two new algorithms name {\tt CAPS} and {\tt CAPSO}. {\tt CAPSO} builds a pyramid starting with an order given on the set of the individuals (or symbolic objects) while {\tt CAPS} finds this order. These two algorithms allows moreover to cluster more complex data than the tabular model allows to process, by considering variation on the values taken by the variables, in this way, our method produces a symbolic pyramid. Each cluster thus formed is defined not only by the set of its elements (i.e. its extent) but also by a symbolic object, which describes its properties (i.e. its intent). These two algorithms were implemented in C++ and Java to the ISO-3D project.
Non-negative two-part outcomes are defined as outcomes with a density function that have a zero point mass but are otherwise positive. Examples, such as healthcare expenditure and hospital length of stay, are common in healthcare utilization research. Despite the practical relevance of non-negative two-part outcomes, very few methods exist to leverage knowledge of their semicontinuity to achieve improved performance in estimating causal effects. In this paper, we develop a nonparametric two-step targeted minimum-loss based estimator (denoted as hTMLE) for non-negative two-part outcomes. We present methods for a general class of interventions referred to as modified treatment policies, which can accommodate continuous, categorical, and binary exposures. The two-step TMLE uses a targeted estimate of the intensity component of the outcome to produce a targeted estimate of the binary component of the outcome that may improve finite sample efficiency. We demonstrate the efficiency gains achieved by the two-step TMLE with simulated examples and then apply it to a cohort of Medicaid beneficiaries to estimate the effect of chronic pain and physical disability on days' supply of opioids.
Advances in artificial intelligence often stem from the development of new environments that abstract real-world situations into a form where research can be done conveniently. This paper contributes such an environment based on ideas inspired by elementary Microeconomics. Agents learn to produce resources in a spatially complex world, trade them with one another, and consume those that they prefer. We show that the emergent production, consumption, and pricing behaviors respond to environmental conditions in the directions predicted by supply and demand shifts in Microeconomics. We also demonstrate settings where the agents' emergent prices for goods vary over space, reflecting the local abundance of goods. After the price disparities emerge, some agents then discover a niche of transporting goods between regions with different prevailing prices -- a profitable strategy because they can buy goods where they are cheap and sell them where they are expensive. Finally, in a series of ablation experiments, we investigate how choices in the environmental rewards, bartering actions, agent architecture, and ability to consume tradable goods can either aid or inhibit the emergence of this economic behavior. This work is part of the environment development branch of a research program that aims to build human-like artificial general intelligence through multi-agent interactions in simulated societies. By exploring which environment features are needed for the basic phenomena of elementary microeconomics to emerge automatically from learning, we arrive at an environment that differs from those studied in prior multi-agent reinforcement learning work along several dimensions. For example, the model incorporates heterogeneous tastes and physical abilities, and agents negotiate with one another as a grounded form of communication.
Humans can naturally and effectively find salient regions in complex scenes. Motivated by this observation, attention mechanisms were introduced into computer vision with the aim of imitating this aspect of the human visual system. Such an attention mechanism can be regarded as a dynamic weight adjustment process based on features of the input image. Attention mechanisms have achieved great success in many visual tasks, including image classification, object detection, semantic segmentation, video understanding, image generation, 3D vision, multi-modal tasks and self-supervised learning. In this survey, we provide a comprehensive review of various attention mechanisms in computer vision and categorize them according to approach, such as channel attention, spatial attention, temporal attention and branch attention; a related repository //github.com/MenghaoGuo/Awesome-Vision-Attentions is dedicated to collecting related work. We also suggest future directions for attention mechanism research.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191