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The analysis of the proteome overall requires comprehensive fractionation to reduce sample complexity, but unmodified peptides tend to elute in the flow-through in methods that selectively enrich the concentration of modified peptides.
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There is also benefit in sample complexity to adding hidden layers, but this is a smaller effect.
Chromosome sorting by flow cytometry can reduce sample complexity and simplify the sequencing of complex genomes by dividing these genomes into smaller parts.
While the universal approximation property holds both for hierarchical and shallow networks, deep networks can approximate the class of compositional functions as well as shallow networks but with exponentially lower number of training parameters and sample complexity.
However, sample complexity of these methods remains very high.
The percentage of pools in which at least one false positive was identified increased with increasing sample complexity (Fig. 2).
Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, and Stephen Tu. "On the Sample Complexity of the Linear Quadratic Regulator". arXiv 1710.01688.
In contrast, learning-based methods improve as the robot acts in the environment, but are difficult to deploy in the real-world due to their high sample complexity.
The sample complexity of a learning task is increased by transformations that do not change class identity.
As an alternative to explicit programming for robots, Deep Imitation learning has two drawbacks: sample complexity and covariate shift.
– Eluder Dimension and the Sample Complexity of Optimistic Exploration by Daniel Russo and Benjamin Van Roy; Prior-free and prior-dependent regret bounds for Thompson Sampling by myself and Che-Yu Liu.
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