If you are predicting the labely of a new object withˆy, how confident are you that y = ˆy?

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A core aspect of intelligence is the ability to quickly learn new tasks by drawing upon prior experience from related tasks. Recent work has studied how meta-learning algorithms [51, 55, 41] can acquire such a capability by learning to efficiently learn a range of tasks, thereby enabling learning of a new task with as little as a single example [50, 57, 15].

Neural Information Processing Systems http://nips.cc/

In the methods, they stick to a single static memory construction policy, which is prone to failing in the long task sequence.

Spectral clustering algorithms provide approximate solutions to hard optimization problems that formulate graph partitioning in terms of the graph conductance. It is well understood that the quality of these approximate solutions is negatively affected by a possibly significant gap between the conductance and the second eigenvalue of the graph. In this paper we show that for \textbf{any} graph $G$, there exists a `spectral maximizer' graph $H$ which is cut-similar to $G$, but has eigenvalues that are near the theoretical limit implied by the cut structure of $G$. Applying then spectral clustering on $H$ has the potential to produce improved cuts that also exist in $G$ due to the cut similarity. This leads to the second contribution of this work: we describe a practical spectral modification algorithm that raises the eigenvalues of the input graph, while preserving its cuts. Combined with spectral clustering on the modified graph, this yields demonstrably improved cuts.

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for large-scale instances. Machine learning frameworks that learn to approximate solutions to such hard optimization problems are a potentially promising avenue to address these difficulties, particularly when many closely related problem instances must be solved repeatedly. Supervised learning frameworks can train a model using the outputs of pre-solved instances. However, when the outputs are themselves approximations, when the optimization problem has symmetric solutions, and/or when the solver uses randomization, solutions to closely related instances may exhibit large differences and the learning task can become inherently more difficult. This paper demonstrates this critical challenge, connects the volatility of the training data to the ability of a model to approximate it, and proposes a method for producing (exact or approximate) solutions to optimization problems that are more amenable to supervised learning tasks. The effectiveness of the method is tested on hard non-linear nonconvex and discrete combinatorial problems.

We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring.