Creating large-scale and well-annotated datasets to train AI algorithms is crucial for automated tumor detection and localization. However, with limited resources, it is challenging to determine the best type of annotations when annotating massive amounts of unlabeled data. To address this issue, we focus on polyps in colonoscopy videos and pancreatic tumors in abdominal CT scans; both applications require significant effort and time for pixel-wise annotation due to the high dimensional nature of the data, involving either temporary or spatial dimensions. In this paper, we develop a new annotation strategy, termed Drag&Drop, which simplifies the annotation process to drag and drop. This annotation strategy is more efficient, particularly for temporal and volumetric imaging, than other types of weak annotations, such as per-pixel, bounding boxes, scribbles, ellipses, and points. Furthermore, to exploit our Drag&Drop annotations, we develop a novel weakly supervised learning method based on the watershed algorithm. Experimental results show that our method achieves better detection and localization performance than alternative weak annotations and, more importantly, achieves similar performance to that trained on detailed per-pixel annotations. Interestingly, we find that, with limited resources, allocating weak annotations from a diverse patient population can foster models more robust to unseen images than allocating per-pixel annotations for a small set of images. In summary, this research proposes an efficient annotation strategy for tumor detection and localization that is less accurate than per-pixel annotations but useful for creating large-scale datasets for screening tumors in various medical modalities.
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The multiobjective evolutionary optimization algorithm (MOEA) is a powerful approach for tackling multiobjective optimization problems (MOPs), which can find a finite set of approximate Pareto solutions in a single run. However, under mild regularity conditions, the Pareto optimal set of a continuous MOP could be a low dimensional continuous manifold that contains infinite solutions. In addition, structure constraints on the whole optimal solution set, which characterize the patterns shared among all solutions, could be required in many real-life applications. It is very challenging for existing finite population based MOEAs to handle these structure constraints properly. In this work, we propose the first model-based algorithmic framework to learn the whole solution set with structure constraints for multiobjective optimization. In our approach, the Pareto optimality can be traded off with a preferred structure among the whole solution set, which could be crucial for many real-world problems. We also develop an efficient evolutionary learning method to train the set model with structure constraints. Experimental studies on benchmark test suites and real-world application problems demonstrate the promising performance of our proposed framework.
In fairness audits, a standard objective is to detect whether a given algorithm performs substantially differently between subgroups. Properly powering the statistical analysis of such audits is crucial for obtaining informative fairness assessments, as it ensures a high probability of detecting unfairness when it exists. However, limited guidance is available on the amount of data necessary for a fairness audit, lacking directly applicable results concerning commonly used fairness metrics. Additionally, the consideration of unequal subgroup sample sizes is also missing. In this tutorial, we address these issues by providing guidance on how to determine the required subgroup sample sizes to maximize the statistical power of hypothesis tests for detecting unfairness. Our findings are applicable to audits of binary classification models and multiple fairness metrics derived as summaries of the confusion matrix. Furthermore, we discuss other aspects of audit study designs that can increase the reliability of audit results.
We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex body have been known now for several decades, but the corresponding deterministic counterparts are not available, and our algorithm is the first of this kind. The class of polytopes for which our algorithm applies arises as linear programming relaxation of the independent set problem with the additional restriction that each variable takes value in the interval $[0,1-\alpha]$ for some $\alpha<1/2$. (We note that the $\alpha\ge 1/2$ case is trivial). We use the correlation decay method for this problem applied to its appropriate and natural discretization. The method works provided $\alpha> 1/2-O(1/\Delta^2)$, where $\Delta$ is the maximum degree of the graph. When $\Delta=3$ (the sparsest non-trivial case), our method works provided $0.488<\alpha<0.5$. Interestingly, the interpolation method, which is based on analyzing complex roots of the associated partition functions, fails even in the trivial case when the underlying graph is a singleton.
Reliable and efficient trajectory optimization methods are a fundamental need for autonomous dynamical systems, effectively enabling applications including rocket landing, hypersonic reentry, spacecraft rendezvous, and docking. Within such safety-critical application areas, the complexity of the emerging trajectory optimization problems has motivated the application of AI-based techniques to enhance the performance of traditional approaches. However, current AI-based methods either attempt to fully replace traditional control algorithms, thus lacking constraint satisfaction guarantees and incurring in expensive simulation, or aim to solely imitate the behavior of traditional methods via supervised learning. To address these limitations, this paper proposes the Autonomous Rendezvous Transformer (ART) and assesses the capability of modern generative models to solve complex trajectory optimization problems, both from a forecasting and control standpoint. Specifically, this work assesses the capabilities of Transformers to (i) learn near-optimal policies from previously collected data, and (ii) warm-start a sequential optimizer for the solution of non-convex optimal control problems, thus guaranteeing hard constraint satisfaction. From a forecasting perspective, results highlight how ART outperforms other learning-based architectures at predicting known fuel-optimal trajectories. From a control perspective, empirical analyses show how policies learned through Transformers are able to generate near-optimal warm-starts, achieving trajectories that are (i) more fuel-efficient, (ii) obtained in fewer sequential optimizer iterations, and (iii) computed with an overall runtime comparable to benchmarks based on convex optimization.
We study functional dependencies together with two different probabilistic dependency notions: unary marginal identity and unary marginal distribution equivalence. A unary marginal identity states that two variables x and y are identically distributed. A unary marginal distribution equivalence states that the multiset consisting of the marginal probabilities of all the values for variable x is the same as the corresponding multiset for y. We present a sound and complete axiomatization for the class of these dependencies and show that it has Armstrong relations. The axiomatization is infinite, but we show that there can be no finite axiomatization. The implication problem for the subclass that contains only functional dependencies and unary marginal identities can be simulated with functional dependencies and unary inclusion atoms, and therefore the problem is in polynomial-time. This complexity bound also holds in the case of the full class, which we show by constructing a polynomial-time algorithm.
Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral preconditioning is an important tool to speed-up the convergence of such iterative algorithms for training kernel models. However computing and storing a spectral preconditioner can be expensive which can lead to large computational and storage overheads, precluding the application of kernel methods to problems with large datasets. A Nystrom approximation of the spectral preconditioner is often cheaper to compute and store, and has demonstrated success in practical applications. In this paper we analyze the trade-offs of using such an approximated preconditioner. Specifically, we show that a sample of logarithmic size (as a function of the size of the dataset) enables the Nystrom-based approximated preconditioner to accelerate gradient descent nearly as well as the exact preconditioner, while also reducing the computational and storage overheads.
Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient complexity for minimizing an $L$-smooth $\mu$-strongly convex objective. However, an ideal algorithm would adapt to the explicit complexity of a particular objective function and incur faster rates for simpler problems, triggering our reconsideration of two defeats of existing optimization modeling and analysis. (i) The worst-case optimality is neither the instance optimality nor such one in reality. (ii) Traditional $L$-smoothness condition may not be the primary abstraction/characterization for modern practical problems. In this paper, we open up a new way to design and analyze gradient-based algorithms with direct applications in machine learning, including linear regression and beyond. We introduce two factors $(\alpha, \tau_{\alpha})$ to refine the description of the degenerated condition of the optimization problems based on the observation that the singular values of Hessian often drop sharply. We design adaptive algorithms that solve simpler problems without pre-known knowledge with reduced gradient or analogous oracle accesses. The algorithms also improve the state-of-art complexities for several problems in machine learning, thereby solving the open problem of how to design faster algorithms in light of the known complexity lower bounds. Specially, with the $\mathcal{O}(1)$-nuclear norm bounded, we achieve an optimal $\tilde{\mathcal{O}}(\mu^{-1/3})$ (v.s. $\tilde{\mathcal{O}}(\mu^{-1/2})$) gradient complexity for linear regression. We hope this work could invoke the rethinking for understanding the difficulty of modern problems in optimization.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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