Digital health data are multimodal and high-dimensional. A patient’s health state can be characterized by a multitude of signals including medical imaging, clinical variables, genome sequencing, conversations between clinicians and patients, and continuous signals from wearables, among others. This high volume, personalized data stream aggregated over patients’ lives has spurred interest in developing new artificial intelligence (AI) models for higher-precision diagnosis, prognosis, and tracking. While the promise of these algorithms is undeniable, their dissemination and adoption have been slow, owing partially to unpredictable AI model performance once deployed in the real world. We posit that one of the rate-limiting factors in developing algorithms that generalize to real-world scenarios is the very attribute that makes the data exciting—their high-dimensional nature. This paper considers how the large number of features in vast digital health data can challenge the development of robust AI models—a phenomenon known as “the curse of dimensionality” in statistical learning theory. We provide an overview of the curse of dimensionality in the context of digital health, demonstrate how it can negatively impact out-of-sample performance, and highlight important considerations for researchers and algorithm designers.
In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f . Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments. KANDASAMY, DASARATHY, OLIVA, SCHNEIDER, PÓCZOS n=300 n=3000 1. We present a formalism for multi-fidelity bandit optimisation using Gaussian process (GP) assumptions on f and its approximations. We develop a novel algorithm, Multi-Fidelity Gaussian Process Upper Confidence Bound (MF-GP-UCB) for this setting.2. Our theoretical analysis proves that MF-GP-UCB explores the space X at lower fidelities and uses the high fidelities in successively smaller regions to converge on the optimum. As lower fidelity queries are cheaper, MF-GP-UCB has better upper bounds on the regret than single fidelity strategies which have to rely on the expensive function to explore the entire space.3. We demonstrate that MF-GP-UCB outperforms single fidelity methods and other alternatives empirically, via a series of synthetic examples, three hyper-parameter tuning tasks and one inference problem in astrophysics. Our matlab implementation and experiments are available at github.com/kirthevasank/mf-gp-ucb. Related WorkSince the seminal work by Robbins [1952], the multi-armed bandit problem has been studied extensively in the K-armed setting. Recently, there has been a surge of interest in the optimism under uncertainty principle for K-armed bandits, typified by upper confidence bound (UCB) methods Cesa-Bianchi, 2012, Auer, 2003]. UCB strategies have also been used in bandit
Abstract-Accurate and timely identification of the routerlevel topology of the Internet is one of the major unresolved problems in Internet research. Topology recovery via tomographic inference is potentially an attractive complement to standard methods that use TTL-limited probes. In this paper, we describe new techniques that aim toward the practical use of tomographic inference for accurate router-level topology measurement. Specifically, prior tomographic techniques have required an infeasible number of probes for accurate, large scale topology recovery. We introduce a Depth-First Search (DFS) Ordering algorithm that clusters end host probe targets based on shared infrastructure, and enables the logical tree topology of the network to be recovered accurately and efficiently. We evaluate the capabilities of our DFS Ordering topology recovery algorithm in simulation and find that our method uses 94% fewer probes than exhaustive methods and 50% fewer than the current state-of-the-art. We also present results from a case study in the live Internet where we show that DFS Ordering can recover the logical router-level topology more accurately and with fewer probes than prior techniques.
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