Athletes routinely undergo fitness evaluations to evaluate their training progress. Typically, these evaluations require a trained professional who utilizes specialized equipment like force plates. For the assessment, athletes perform drop and squat jumps, and key variables are measured, e.g. velocity, flight time, and time to stabilization, to name a few. However, amateur athletes may not have access to professionals or equipment that can provide these assessments. Here, we investigate the feasibility of estimating key variables using video recordings. We focus on jump velocity as a starting point because it is highly correlated with other key variables and is important for determining posture and lower-limb capacity. We find that velocity can be estimated with a high degree of precision across a range of athletes, with an average R-value of 0.71 (SD = 0.06).
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Zero-shot coordination in cooperative artificial intelligence (AI) remains a significant challenge, which means effectively coordinating with a wide range of unseen partners. Previous algorithms have attempted to address this challenge by optimizing fixed objectives within a population to improve strategy or behavior diversity. However, these approaches can result in a loss of learning and an inability to cooperate with certain strategies within the population, known as cooperative incompatibility. To address this issue, we propose the Cooperative Open-ended LEarning (COLE) framework, which constructs open-ended objectives in cooperative games with two players from the perspective of graph theory to assess and identify the cooperative ability of each strategy. We further specify the framework and propose a practical algorithm that leverages knowledge from game theory and graph theory. Furthermore, an analysis of the learning process of the algorithm shows that it can efficiently overcome cooperative incompatibility. The experimental results in the Overcooked game environment demonstrate that our method outperforms current state-of-the-art methods when coordinating with different-level partners. Our code and demo are available at //sites.google.com/view/cole-2023.
Self-paced curriculum learning (SCL) has demonstrated its great potential in computer vision, natural language processing, etc. During training, it implements easy-to-hard sampling based on online estimation of data difficulty. Most SCL methods commonly adopt a loss-based strategy of estimating data difficulty and deweighting the `hard' samples in the early training stage. While achieving success in a variety of applications, SCL stills confront two challenges in a medical image analysis task, such as universal lesion detection, featuring insufficient and highly class-imbalanced data: (i) the loss-based difficulty measurer is inaccurate; ii) the hard samples are under-utilized from a deweighting mechanism. To overcome these challenges, in this paper we propose a novel mixed-order self-paced curriculum learning (Mo-SCL) method. We integrate both uncertainty and loss to better estimate difficulty online and mix both hard and easy samples in the same mini-batch to appropriately alleviate the problem of under-utilization of hard samples. We provide a theoretical investigation of our method in the context of stochastic gradient descent optimization and extensive experiments based on the DeepLesion benchmark dataset for universal lesion detection (ULD). When applied to two state-of-the-art ULD methods, the proposed mixed-order SCL method can provide a free boost to lesion detection accuracy without extra special network designs.
Suppose we are given access to $n$ independent samples from distribution $\mu$ and we wish to output one of them with the goal of making the output distributed as close as possible to a target distribution $\nu$. In this work we show that the optimal total variation distance as a function of $n$ is given by $\tilde\Theta(\frac{D}{f'(n)})$ over the class of all pairs $\nu,\mu$ with a bounded $f$-divergence $D_f(\nu\|\mu)\leq D$. Previously, this question was studied only for the case when the Radon-Nikodym derivative of $\nu$ with respect to $\mu$ is uniformly bounded. We then consider an application in the seemingly very different field of smoothed online learning, where we show that recent results on the minimax regret and the regret of oracle-efficient algorithms still hold even under relaxed constraints on the adversary (to have bounded $f$-divergence, as opposed to bounded Radon-Nikodym derivative). Finally, we also study efficacy of importance sampling for mean estimates uniform over a function class and compare importance sampling with rejection sampling.
Motivated by a real-world application, we model and solve a complex staff scheduling problem. Tasks are to be assigned to workers for supervision. Multiple tasks can be covered in parallel by a single worker, with worker shifts being flexible within availabilities. Each worker has a different skill set, enabling them to cover different tasks. Tasks require assignment according to priority and skill requirements. The objective is to maximize the number of assigned tasks weighted by their priorities, while minimizing assignment penalties. We develop an adaptive large neighborhood search (ALNS) algorithm, relying on tailored destroy and repair operators. It is tested on benchmark instances derived from real-world data and compared to optimal results obtained by means of a commercial MIP-solver. Furthermore, we analyze the impact of considering three additional alternative objective functions. When applied to large-scale company data, the developed ALNS outperforms the previously applied solution approach.
While most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases the diversity of the final solution set. When compared with two existing methods, our method runs with similar runtime as regular node selection methods and gives a diversity improvement between 12% and 190%. In contrast, popular node selection rules, such as best-first search, in some instances performed worse than state-of-the-art methods by more than 35% and gave an improvement of no more than 130%. Further, we find that our method is most effective when diversity in node selection is continuously emphasized after reaching a minimal depth in the tree and when the solution set has grown sufficiently large. Our method can be easily incorporated into integer programming solvers and has the potential to significantly increase the diversity of solution sets.
Privacy auditing techniques for differentially private (DP) algorithms are useful for estimating the privacy loss to compare against analytical bounds, or empirically measure privacy in settings where known analytical bounds on the DP loss are not tight. However, existing privacy auditing techniques usually make strong assumptions on the adversary (e.g., knowledge of intermediate model iterates or the training data distribution), are tailored to specific tasks and model architectures, and require retraining the model many times (typically on the order of thousands). These shortcomings make deploying such techniques at scale difficult in practice, especially in federated settings where model training can take days or weeks. In this work, we present a novel "one-shot" approach that can systematically address these challenges, allowing efficient auditing or estimation of the privacy loss of a model during the same, single training run used to fit model parameters. Our privacy auditing method for federated learning does not require a priori knowledge about the model architecture or task. We show that our method provides provably correct estimates for privacy loss under the Gaussian mechanism, and we demonstrate its performance on a well-established FL benchmark dataset under several adversarial models.
Full Waveform Inversion (FWI) is a large-scale nonlinear ill-posed problem for which implementation of the Newton-type methods is computationally expensive. Moreover, these methods can trap in undesirable local minima when the starting model lacks low-wavenumber part and the recorded data lack low-frequency content. In this paper, the Gauss-Newton (GN) method is modified to address these issues. We rewrite the GN system for multisoure multireceiver FWI in an equivalent matrix equation form whose solution is a diagonal matrix, instead of a vector in the standard system. Then we relax the diagonality constraint, lifting the search direction from a vector to a matrix. This relaxation is equivalent to introducing an extra degree of freedom in the subsurface offset axis for the search direction. Furthermore, it makes the Hessian matrix separable and easy to invert. The relaxed system is solved explicitly for computing the desired search direction, requiring only inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions. Application of the Extended GN (EGN) method to solve the extended-source FWI leads to an algorithm that has the advantages of both model extension and source extension. Numerical examples are presented showing robustness and stability of EGN algorithm for waveform inversion.
Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notations, and the convergence estimates that are available are difficult to compare. We describe Parareal, PFASST, MGRIT and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge super-linearly, and also compare them numerically. The generating function framework provides further opportunities to explore and analyze existing and new methods.
We consider \emph{Gibbs distributions}, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval $[\beta_{\min}, \beta_{\max}]$ and $H( \omega ) \in \{0 \} \cup [1, n]$. The \emph{partition function} is the normalization factor $Z(\beta)=\sum_{\omega \in\Omega}e^{\beta H(\omega)}$. Two important parameters of these distributions are the log partition ratio $q = \log \tfrac{Z(\beta_{\max})}{Z(\beta_{\min})}$ and the counts $c_x = |H^{-1}(x)|$. These are correlated with system parameters in a number of physical applications and sampling algorithms. Our first main result is to estimate the counts $c_x$ using roughly $\tilde O( \frac{q}{\varepsilon^2})$ samples for general Gibbs distributions and $\tilde O( \frac{n^2}{\varepsilon^2} )$ samples for integer-valued distributions (ignoring some second-order terms and parameters), and we show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs and perfect matchings in a graph. We develop a key subroutine to estimate the partition function $Z$. Specifically, it generates a data structure to estimate $Z(\beta)$ for \emph{all} values $\beta$, without further samples. Constructing the data structure requires $O(\frac{q \log n}{\varepsilon^2})$ samples for general Gibbs distributions and $O(\frac{n^2 \log n}{\varepsilon^2} + n \log q)$ samples for integer-valued distributions. This improves over a prior algorithm of Huber (2015) which computes a single point estimate $Z(\beta_\max)$ using $O( q \log n( \log q + \log \log n + \varepsilon^{-2}))$ samples. We show matching lower bounds, demonstrating that this complexity is optimal as a function of $n$ and $q$ up to logarithmic terms.
Convolutional neural networks (CNNs) have shown dramatic improvements in single image super-resolution (SISR) by using large-scale external samples. Despite their remarkable performance based on the external dataset, they cannot exploit internal information within a specific image. Another problem is that they are applicable only to the specific condition of data that they are supervised. For instance, the low-resolution (LR) image should be a "bicubic" downsampled noise-free image from a high-resolution (HR) one. To address both issues, zero-shot super-resolution (ZSSR) has been proposed for flexible internal learning. However, they require thousands of gradient updates, i.e., long inference time. In this paper, we present Meta-Transfer Learning for Zero-Shot Super-Resolution (MZSR), which leverages ZSSR. Precisely, it is based on finding a generic initial parameter that is suitable for internal learning. Thus, we can exploit both external and internal information, where one single gradient update can yield quite considerable results. (See Figure 1). With our method, the network can quickly adapt to a given image condition. In this respect, our method can be applied to a large spectrum of image conditions within a fast adaptation process.
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