1,059 research outputs found
Proximal Online Gradient is Optimum for Dynamic Regret
In online learning, the dynamic regret metric chooses the reference (optimal)
solution that may change over time, while the typical (static) regret metric
assumes the reference solution to be constant over the whole time horizon. The
dynamic regret metric is particularly interesting for applications such as
online recommendation (since the customers' preference always evolves over
time). While the online gradient method has been shown to be optimal for the
static regret metric, the optimal algorithm for the dynamic regret remains
unknown. In this paper, we show that proximal online gradient (a general
version of online gradient) is optimum to the dynamic regret by showing that
the proved lower bound matches the upper bound that slightly improves existing
upper bound
Enabling Covariance-Based Feedback in Massive MIMO: A User Classification Approach
In this paper, we propose a novel channel feedback scheme for frequency
division duplexing massive multi-input multi-output systems. The concept uses
the notion of user statistical separability which was hinted in several prior
works in the massive antenna regime but not fully exploited so far. We here
propose a hybrid statistical-instantaneous feedback scheme based on a user
classification mechanism where the classification metric derives from a rate
bound analysis. According to classification results, a user either operates on
a statistical feedback mode or instantaneous mode. Our results illustrate the
sum rate advantages of our scheme under a global feedback overhead constraint.Comment: 5 pages, 4 figures, conference paper, 2018 Asilomar Conference on
Signals, Systems, and Computer
Constructing black holes in Einstein-Maxwell-scalar theory
Exact black hole solutions in the Einstein-Maxwell-scalar theory are
constructed. They are the extensions of dilaton black holes in de Sitter or
anti de Sitter universe. As a result, except for a scalar potential, a coupling
function between the scalar field and the Maxwell invariant is present. Then
the corresponding Smarr formula and the first law of thermodynamics are
investigated.Comment: 25 pages,8 figure
The Second Order Linear Model
We study a fundamental class of regression models called the second order
linear model (SLM). The SLM extends the linear model to high order functional
space and has attracted considerable research interest recently. Yet how to
efficiently learn the SLM under full generality using nonconvex solver still
remains an open question due to several fundamental limitations of the
conventional gradient descent learning framework. In this study, we try to
attack this problem from a gradient-free approach which we call the
moment-estimation-sequence (MES) method. We show that the conventional gradient
descent heuristic is biased by the skewness of the distribution therefore is no
longer the best practice of learning the SLM. Based on the MES framework, we
design a nonconvex alternating iteration process to train a -dimension
rank- SLM within memory and one-pass of the dataset. The proposed
method converges globally and linearly, achieves recovery error
after retrieving samples.
Furthermore, our theoretical analysis reveals that not all SLMs can be learned
on every sub-gaussian distribution. When the instances are sampled from a
so-called -MIP distribution, the SLM can be learned by
samples where and are positive constants depending on the skewness
and kurtosis of the distribution. For non-MIP distribution, an addition
diagonal-free oracle is necessary and sufficient to guarantee the learnability
of the SLM. Numerical simulations verify the sharpness of our bounds on the
sampling complexity and the linear convergence rate of our algorithm
Nonconvex One-bit Single-label Multi-label Learning
We study an extreme scenario in multi-label learning where each training
instance is endowed with a single one-bit label out of multiple labels. We
formulate this problem as a non-trivial special case of one-bit rank-one matrix
sensing and develop an efficient non-convex algorithm based on alternating
power iteration. The proposed algorithm is able to recover the underlying
low-rank matrix model with linear convergence. For a rank- model with
features and classes, the proposed algorithm achieves
recovery error after retrieving one-bit labels
within memory. Our bound is nearly optimal in the order of
. This significantly improves the state-of-the-art sampling
complexity of one-bit multi-label learning. We perform experiments to verify
our theory and evaluate the performance of the proposed algorithm
A Covariance-Based Hybrid Channel Feedback in FDD Massive MIMO Systems
In this paper, a novel covariance-based channel feedback mechanism is
investigated for frequency division duplexing (FDD) massive multi-input
multi-output (MIMO) systems. The concept capitalizes on the notion of user
statistical separability which was hinted in several prior works in the massive
antenna regime but not fully exploited so far. We here propose a hybrid
statistical-instantaneous feedback mechanism where the users are separated into
two classes of feedback design based on their channel covariance. Under the
hybrid framework, each user either operates on a statistical feedback mode or
quantized instantaneous channel feedback mode depending on their so-called
statistical isolability. The key challenge lies in the design of a
covariance-aware classification algorithm which can handle the complex mutual
interactions between all users. The classification is derived from rate bound
principles. A suitable precoding method is also devised under the mixed
statistical and instantaneous feedback model. Simulations are performed to
validate our analytical results and illustrate the sum rate advantages of the
proposed feedback scheme under a global feedback overhead constraint.Comment: 31 pages, 9 figure
Walking behavior in a circular arena modified by pulsed light stimulation in Drosophila melanogaster w1118 line
The Drosophila melanogaster white-eyed w1118 line serves as a blank control,
allowing genetic recombination of any gene of interest along with a readily
recognizable marker. w1118 flies display behavioral susceptibility to
environmental stimulation such as light. It is of great importance to
characterize the behavioral performance of w1118 flies because this would
provide a baseline from which the effect of the gene of interest could be
differentiated. Little work has been performed to characterize the walking
behavior in adult w1118 flies. Here we show that pulsed light stimulation
increased the regularity of walking trajectories of w1118 flies in circular
arenas. We statistically modeled the distribution of distances to center and
extracted the walking structures of w1118 flies. Pulsed light stimulation
redistributed the time proportions for individual walking structures.
Specifically, pulsed light stimulation reduced the episodes of crossing over
the central region of the arena. An addition of four genomic copies of
mini-white, a common marker gene for eye color, mimicked the effect of pulsed
light stimulation in reducing crossing in a circular arena. The reducing effect
of mini-white was copy-number-dependent. These findings highlight the rhythmic
light stimulation-evoked modifications of walking behavior in w1118 flies and
an unexpected behavioral consequence of mini-white in transgenic flies carrying
w1118 isogenic background.Comment: 27 pages, 6 figures, research articl
Creation of Ghost Illusions Using Metamaterials in Wave Dynamics
The creation of wave-dynamic illusion functionality is of great interests to
various scientific communities, which can potentially transform an actual
perception into the pre-controlled perception, thus empowering unprecedented
applications in the advanced-material science, camouflage, cloaking, optical
and/or microwave cognition, and defense security, etc. By using the space
transformation theory and engineering capability of metamaterials, we propose
and realize a functional ghost illusion device, which is capable of creating
wave-dynamic virtual ghost images off the original object's position under the
illumination of electromagnetic waves. The scattering signature of the object
is thus ghosted and perceived as multiple ghost targets with different
geometries and compositions. The ghost-illusion material, being inhomogeneous
and anisotropic, was realized by thousands of varying unit cells working at
non-resonance. The experimental demonstration of the ghost illusion validates
our theory of scattering metamorphosis and opens a novel avenue to the
wave-dynamic illusion, cognitive deception, manipulate strange light or matter
behaviors, and design novel optical and microwave devices.Comment: 19 pages, 6 figure
GESF: A Universal Discriminative Mapping Mechanism for Graph Representation Learning
Graph embedding is a central problem in social network analysis and many
other applications, aiming to learn the vector representation for each node.
While most existing approaches need to specify the neighborhood and the
dependence form to the neighborhood, which may significantly degrades the
flexibility of representation, we propose a novel graph node embedding method
(namely GESF) via the set function technique. Our method can 1) learn an
arbitrary form of representation function from neighborhood, 2) automatically
decide the significance of neighbors at different distances, and 3) be applied
to heterogeneous graph embedding, which may contain multiple types of nodes.
Theoretical guarantee for the representation capability of our method has been
proved for general homogeneous and heterogeneous graphs and evaluation results
on benchmark data sets show that the proposed GESF outperforms the
state-of-the-art approaches on producing node vectors for classification tasks.Comment: 18 page
Decentralized Online Learning: Take Benefits from Others' Data without Sharing Your Own to Track Global Trend
Decentralized Online Learning (online learning in decentralized networks)
attracts more and more attention, since it is believed that Decentralized
Online Learning can help the data providers cooperatively better solve their
online problems without sharing their private data to a third party or other
providers. Typically, the cooperation is achieved by letting the data providers
exchange their models between neighbors, e.g., recommendation model. However,
the best regret bound for a decentralized online learning algorithm is
\Ocal{n\sqrt{T}}, where is the number of nodes (or users) and is the
number of iterations. This is clearly insignificant since this bound can be
achieved \emph{without} any communication in the networks. This reminds us to
ask a fundamental question: \emph{Can people really get benefit from the
decentralized online learning by exchanging information?} In this paper, we
studied when and why the communication can help the decentralized online
learning to reduce the regret. Specifically, each loss function is
characterized by two components: the adversarial component and the stochastic
component. Under this characterization, we show that decentralized online
gradient (DOG) enjoys a regret bound \Ocal{n\sqrt{T}G + \sqrt{nT}\sigma},
where measures the magnitude of the adversarial component in the private
data (or equivalently the local loss function) and measures the
randomness within the private data. This regret suggests that people can get
benefits from the randomness in the private data by exchanging private
information. Another important contribution of this paper is to consider the
dynamic regret -- a more practical regret to track users' interest dynamics.
Empirical studies are also conducted to validate our analysis.Comment: Second version: revise Assumption 1 (there is a typo in the first
version); add experiments (see Figure 2); revise Algorithm 1 in a more clear
wa
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