317 research outputs found
Learning Unitary Operators with Help From u(n)
A major challenge in the training of recurrent neural networks is the
so-called vanishing or exploding gradient problem. The use of a norm-preserving
transition operator can address this issue, but parametrization is challenging.
In this work we focus on unitary operators and describe a parametrization using
the Lie algebra associated with the Lie group of unitary matrices. The exponential map provides a correspondence
between these spaces, and allows us to define a unitary matrix using real
coefficients relative to a basis of the Lie algebra. The parametrization is
closed under additive updates of these coefficients, and thus provides a simple
space in which to do gradient descent. We demonstrate the effectiveness of this
parametrization on the problem of learning arbitrary unitary operators,
comparing to several baselines and outperforming a recently-proposed
lower-dimensional parametrization. We additionally use our parametrization to
generalize a recently-proposed unitary recurrent neural network to arbitrary
unitary matrices, using it to solve standard long-memory tasks.Comment: 9 pages, 3 figures, 5 figures inc. subfigures, to appear at AAAI-1
A Generative Model of Words and Relationships from Multiple Sources
Neural language models are a powerful tool to embed words into semantic
vector spaces. However, learning such models generally relies on the
availability of abundant and diverse training examples. In highly specialised
domains this requirement may not be met due to difficulties in obtaining a
large corpus, or the limited range of expression in average use. Such domains
may encode prior knowledge about entities in a knowledge base or ontology. We
propose a generative model which integrates evidence from diverse data sources,
enabling the sharing of semantic information. We achieve this by generalising
the concept of co-occurrence from distributional semantics to include other
relationships between entities or words, which we model as affine
transformations on the embedding space. We demonstrate the effectiveness of
this approach by outperforming recent models on a link prediction task and
demonstrating its ability to profit from partially or fully unobserved data
training labels. We further demonstrate the usefulness of learning from
different data sources with overlapping vocabularies.Comment: 8 pages, 5 figures; incorporated feedback from reviewers; to appear
in Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence
201
Boosting Variational Inference: an Optimization Perspective
Variational inference is a popular technique to approximate a possibly
intractable Bayesian posterior with a more tractable one. Recently, boosting
variational inference has been proposed as a new paradigm to approximate the
posterior by a mixture of densities by greedily adding components to the
mixture. However, as is the case with many other variational inference
algorithms, its theoretical properties have not been studied. In the present
work, we study the convergence properties of this approach from a modern
optimization viewpoint by establishing connections to the classic Frank-Wolfe
algorithm. Our analyses yields novel theoretical insights regarding the
sufficient conditions for convergence, explicit rates, and algorithmic
simplifications. Since a lot of focus in previous works for variational
inference has been on tractability, our work is especially important as a much
needed attempt to bridge the gap between probabilistic models and their
corresponding theoretical properties
Greedy Algorithms for Cone Constrained Optimization with Convergence Guarantees
Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe
(FW) algorithms regained popularity in recent years due to their simplicity,
effectiveness and theoretical guarantees. MP and FW address optimization over
the linear span and the convex hull of a set of atoms, respectively. In this
paper, we consider the intermediate case of optimization over the convex cone,
parametrized as the conic hull of a generic atom set, leading to the first
principled definitions of non-negative MP algorithms for which we give explicit
convergence rates and demonstrate excellent empirical performance. In
particular, we derive sublinear () convergence on general
smooth and convex objectives, and linear convergence () on
strongly convex objectives, in both cases for general sets of atoms.
Furthermore, we establish a clear correspondence of our algorithms to known
algorithms from the MP and FW literature. Our novel algorithms and analyses
target general atom sets and general objective functions, and hence are
directly applicable to a large variety of learning settings.Comment: NIPS 201
rQuant.web: a tool for RNA-Seq-based transcript quantitation
We provide a novel web service, called rQuant.web, allowing convenient access to tools for quantitative analysis of RNA sequencing data. The underlying quantitation technique rQuant is based on quadratic programming and estimates different biases induced by library preparation, sequencing and read mapping. It can tackle multiple transcripts per gene locus and is therefore particularly well suited to quantify alternative transcripts. rQuant.web is available as a tool in a Galaxy installation at http://galaxy.fml.mpg.de. Using rQuant.web is free of charge, it is open to all users, and there is no login requirement
SOM-VAE: Interpretable Discrete Representation Learning on Time Series
High-dimensional time series are common in many domains. Since human
cognition is not optimized to work well in high-dimensional spaces, these areas
could benefit from interpretable low-dimensional representations. However, most
representation learning algorithms for time series data are difficult to
interpret. This is due to non-intuitive mappings from data features to salient
properties of the representation and non-smoothness over time. To address this
problem, we propose a new representation learning framework building on ideas
from interpretable discrete dimensionality reduction and deep generative
modeling. This framework allows us to learn discrete representations of time
series, which give rise to smooth and interpretable embeddings with superior
clustering performance. We introduce a new way to overcome the
non-differentiability in discrete representation learning and present a
gradient-based version of the traditional self-organizing map algorithm that is
more performant than the original. Furthermore, to allow for a probabilistic
interpretation of our method, we integrate a Markov model in the representation
space. This model uncovers the temporal transition structure, improves
clustering performance even further and provides additional explanatory
insights as well as a natural representation of uncertainty. We evaluate our
model in terms of clustering performance and interpretability on static
(Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST
images, a chaotic Lorenz attractor system with two macro states, as well as on
a challenging real world medical time series application on the eICU data set.
Our learned representations compare favorably with competitor methods and
facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on
Learning Representations (ICLR 2019
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