4,152 research outputs found
Surface Networks
We study data-driven representations for three-dimensional triangle meshes,
which are one of the prevalent objects used to represent 3D geometry. Recent
works have developed models that exploit the intrinsic geometry of manifolds
and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants,
which learn from the local metric tensor via the Laplacian operator. Despite
offering excellent sample complexity and built-in invariances, intrinsic
geometry alone is invariant to isometric deformations, making it unsuitable for
many applications. To overcome this limitation, we propose several upgrades to
GNNs to leverage extrinsic differential geometry properties of
three-dimensional surfaces, increasing its modeling power.
In particular, we propose to exploit the Dirac operator, whose spectrum
detects principal curvature directions --- this is in stark contrast with the
classical Laplace operator, which directly measures mean curvature. We coin the
resulting models \emph{Surface Networks (SN)}. We prove that these models
define shape representations that are stable to deformation and to
discretization, and we demonstrate the efficiency and versatility of SNs on two
challenging tasks: temporal prediction of mesh deformations under non-linear
dynamics and generative models using a variational autoencoder framework with
encoders/decoders given by SNs
An Overview on Application of Machine Learning Techniques in Optical Networks
Today's telecommunication networks have become sources of enormous amounts of
widely heterogeneous data. This information can be retrieved from network
traffic traces, network alarms, signal quality indicators, users' behavioral
data, etc. Advanced mathematical tools are required to extract meaningful
information from these data and take decisions pertaining to the proper
functioning of the networks from the network-generated data. Among these
mathematical tools, Machine Learning (ML) is regarded as one of the most
promising methodological approaches to perform network-data analysis and enable
automated network self-configuration and fault management. The adoption of ML
techniques in the field of optical communication networks is motivated by the
unprecedented growth of network complexity faced by optical networks in the
last few years. Such complexity increase is due to the introduction of a huge
number of adjustable and interdependent system parameters (e.g., routing
configurations, modulation format, symbol rate, coding schemes, etc.) that are
enabled by the usage of coherent transmission/reception technologies, advanced
digital signal processing and compensation of nonlinear effects in optical
fiber propagation. In this paper we provide an overview of the application of
ML to optical communications and networking. We classify and survey relevant
literature dealing with the topic, and we also provide an introductory tutorial
on ML for researchers and practitioners interested in this field. Although a
good number of research papers have recently appeared, the application of ML to
optical networks is still in its infancy: to stimulate further work in this
area, we conclude the paper proposing new possible research directions
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Partition-based Model Representation Learning
Modern machine learning consists of both task forces from classical statistics and modern computation. On the one hand, this field becomes rich and quick-growing; on the other hand, different convention from different schools becomes harder and harder to communicate over time. A lot of the times, the problem is not about who is absolutely right or wrong, but about from which angle that one should approach the problem. This is the moment when we feel there should be a unifying machine learning framework that can withhold different schools under the same umbrella. So we propose one of such a framework and call it ``representation learning''.
Representations are for the data, which is almost identical to a statistical model. However, philosophically, we would like to distinguish from classical statistical modeling such that (1) representations are interpretable to the scientist, (2) representations convey the pre-existing subject view that the scientist has towards his/her data before seeing it (in other words, representations may not align with the true data generating process), and (3) representations are task-oriented.
To build such a representation, we propose to use partition-based models. Partition-based models are easy to interpret and useful for figuring out the interactions between variables. However, the major challenge lies in the computation, since the partition numbers can grow exponentially with respect to the number of variables. To solve the problem, we need a model/representation selection method over different partition models. We proposed to use I-Score with backward dropping algorithm to achieve the goal.
In this work, we explore the connection between the I-Score variable selection methodology to other existing methods and extend the idea into developing other objective functions that can be used in other applications. We apply our ideas to analyze three datasets, one is the genome-wide association study (GWAS), one is the New York City Vision Zero, and, lastly, the MNIST handwritten digit database.
On these applications, we showed the potential of the interpretability of the representations can be useful in practice and provide practitioners with much more intuitions in explaining their results. Also, we showed a novel way to look at causal inference problems from the view of partition-based models.
We hope this work serve as an initiative for people to start thinking about approaching problems from a different angle and to involve interpretability into the consideration when building a model so that it can be easier to be used to communicate with people from other fields
Representation Learning: A Review and New Perspectives
The success of machine learning algorithms generally depends on data
representation, and we hypothesize that this is because different
representations can entangle and hide more or less the different explanatory
factors of variation behind the data. Although specific domain knowledge can be
used to help design representations, learning with generic priors can also be
used, and the quest for AI is motivating the design of more powerful
representation-learning algorithms implementing such priors. This paper reviews
recent work in the area of unsupervised feature learning and deep learning,
covering advances in probabilistic models, auto-encoders, manifold learning,
and deep networks. This motivates longer-term unanswered questions about the
appropriate objectives for learning good representations, for computing
representations (i.e., inference), and the geometrical connections between
representation learning, density estimation and manifold learning
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