instruction:
In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
question:
In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One way to address this question is to find an upper bound on the probability (equivalently a lower bound on the negative log likelihood) that the model can assign to some data as one varies the prior and/or the likelihood function in a latent variable model. The core of our contribution is to formally show that the problem of optimizing priors in latent variable models is exactly an instance of the variational optimization problem that information theorists solve when computing rate-distortion functions, and then to use this to derive a lower bound on negative log likelihood. Moreover, we will show that if changing the prior can improve the log likelihood, then there is a way to change the likelihood function instead and attain the same log likelihood, and thus rate-distortion theory is of relevance to both optimizing priors as well as optimizing likelihood functions. We will experimentally argue for the usefulness of quantities derived from rate-distortion theory in latent variable modeling by applying them to a problem in image modeling.
answer:
Use rate-distortion theory to bound how much a latent variable model can be improved

question:
We introduce NAMSG, an adaptive first-order algorithm for training neural networks. The method is efficient in computation and memory, and is straightforward to implement. It computes the gradients at configurable remote observation points, in order to expedite the convergence by adjusting the step size for directions with different curvatures in the stochastic setting. It also scales the updating vector elementwise by a nonincreasing preconditioner to take the advantages of AMSGRAD. We analyze the convergence properties for both convex and nonconvex problems by modeling the training process as a dynamic system, and provide a strategy to select the observation factor without grid search. A data-dependent regret bound is proposed to guarantee the convergence in the convex setting. The method can further achieve a O(log(T)) regret bound for strongly convex functions. Experiments demonstrate that NAMSG works well in practical problems and compares favorably to popular adaptive methods, such as ADAM, NADAM, and AMSGRAD.
answer:
A new algorithm for training neural networks that compares favorably to popular adaptive methods.

question:
Learning to predict complex time-series data is a fundamental challenge in a range of disciplines including Machine Learning, Robotics, and Natural Language Processing. Predictive State Recurrent Neural Networks (PSRNNs) (Downey et al.) are a state-of-the-art approach for modeling time-series data which combine the benefits of probabilistic filters and Recurrent Neural Networks into a single model. PSRNNs leverage the concept of Hilbert Space Embeddings of distributions (Smola et al.) to embed predictive states into a Reproducing Kernel Hilbert Space, then estimate, predict, and update these embedded states using Kernel Bayes Rule. Practical implementations of PSRNNs are made possible by the machinery of Random Features, where input features are mapped into a new space where dot products approximate the kernel well. Unfortunately PSRNNs often require a large number of RFs to obtain good results, resulting in large models which are slow to execute and slow to train. Orthogonal Random Features (ORFs) (Choromanski et al.) is an improvement on RFs which has been shown to decrease the number of RFs required for pointwise kernel approximation. Unfortunately, it is not clear that ORFs can be applied to PSRNNs, as PSRNNs rely on Kernel Ridge Regression as a core component of their learning algorithm, and the theoretical guarantees of ORF do not apply in this setting. In this paper, we extend the theory of ORFs to Kernel Ridge Regression and show that ORFs can be used to obtain Orthogonal PSRNNs (OPSRNNs), which are smaller and faster than PSRNNs. In particular, we show that OPSRNN models clearly outperform LSTMs and furthermore, can achieve accuracy similar to PSRNNs with an order of magnitude smaller number of features needed.
answer:
Improving Predictive State Recurrent Neural Networks via Orthogonal Random Features