370 research outputs found
Modeling Temporal Data as Continuous Functions with Process Diffusion
Temporal data like time series are often observed at irregular intervals
which is a challenging setting for existing machine learning methods. To tackle
this problem, we view such data as samples from some underlying continuous
function. We then define a diffusion-based generative model that adds noise
from a predefined stochastic process while preserving the continuity of the
resulting underlying function. A neural network is trained to reverse this
process which allows us to sample new realizations from the learned
distribution. We define suitable stochastic processes as noise sources and
introduce novel denoising and score-matching models on processes. Further, we
show how to apply this approach to the multivariate probabilistic forecasting
and imputation tasks. Through our extensive experiments, we demonstrate that
our method outperforms previous models on synthetic and real-world datasets
Do price trajectory data increase the efficiency of market impact estimation?
Market impact is an important problem faced by large institutional investor
and active market participant. In this paper, we rigorously investigate whether
price trajectory data from the metaorder increases the efficiency of
estimation, from an asymptotic view of statistical estimation. We show that,
for popular market impact models, estimation methods based on partial price
trajectory data, especially those containing early trade prices, can outperform
established estimation methods (e.g., VWAP-based) asymptotically. We discuss
theoretical and empirical implications of such phenomenon, and how they could
be readily incorporated into practice
Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes
Many event sequence data exhibit mutually exciting or inhibiting patterns.
Reliable detection of such temporal dependency is crucial for scientific
investigation. The de facto model is the Multivariate Hawkes Process (MHP),
whose impact function naturally encodes a causal structure in Granger
causality. However, the vast majority of existing methods use direct or
nonlinear transform of standard MHP intensity with constant baseline,
inconsistent with real-world data. Under irregular and unknown heterogeneous
intensity, capturing temporal dependency is hard as one struggles to
distinguish the effect of mutual interaction from that of intensity
fluctuation. In this paper, we address the short-term temporal dependency
detection issue. We show the maximum likelihood estimation (MLE) for
cross-impact from MHP has an error that can not be eliminated but may be
reduced by order of magnitude, using heterogeneous intensity not of the target
HP but of the interacting HP. Then we proposed a robust and
computationally-efficient method modified from MLE that does not rely on the
prior estimation of the heterogeneous intensity and is thus applicable in a
data-limited regime (e.g., few-shot, no repeated observations). Extensive
experiments on various datasets show that our method outperforms existing ones
by notable margins, with highlighted novel applications in neuroscience.Comment: Conference on Uncertainty in Artificial Intelligence 202
Learning to Abstain From Uninformative Data
Learning and decision-making in domains with naturally high noise-to-signal
ratio, such as Finance or Healthcare, is often challenging, while the stakes
are very high. In this paper, we study the problem of learning and acting under
a general noisy generative process. In this problem, the data distribution has
a significant proportion of uninformative samples with high noise in the label,
while part of the data contains useful information represented by low label
noise. This dichotomy is present during both training and inference, which
requires the proper handling of uninformative data during both training and
testing. We propose a novel approach to learning under these conditions via a
loss inspired by the selective learning theory. By minimizing this loss, the
model is guaranteed to make a near-optimal decision by distinguishing
informative data from uninformative data and making predictions. We build upon
the strength of our theoretical guarantees by describing an iterative
algorithm, which jointly optimizes both a predictor and a selector, and
evaluates its empirical performance in a variety of settings
Propagation Speed of the Maximum of the Fundamental Solution to the Fractional Diffusion-Wave Equation
In this paper, the one-dimensional time-fractional diffusion-wave equation
with the fractional derivative of order is revisited. This
equation interpolates between the diffusion and the wave equations that behave
quite differently regarding their response to a localized disturbance: whereas
the diffusion equation describes a process, where a disturbance spreads
infinitely fast, the propagation speed of the disturbance is a constant for the
wave equation. For the time fractional diffusion-wave equation, the propagation
speed of a disturbance is infinite, but its fundamental solution possesses a
maximum that disperses with a finite speed. In this paper, the fundamental
solution of the Cauchy problem for the time-fractional diffusion-wave equation,
its maximum location, maximum value, and other important characteristics are
investigated in detail. To illustrate analytical formulas, results of numerical
calculations and plots are presented. Numerical algorithms and programs used to
produce plots are discussed.Comment: 22 pages 6 figures. This paper has been presented by F. Mainardi at
the International Workshop: Fractional Differentiation and its Applications
(FDA12) Hohai University, Nanjing, China, 14-17 May 201
Spanning Fermi arcs in a two-dimensional magnet
The discovery of topological states of matter has led to a revolution in
materials research. When external or intrinsic parameters break certain
symmetries, global properties of topological materials change drastically. A
paramount example is the emergence of Weyl nodes under broken inversion
symmetry, acting like magnetic monopoles in momentum space. However, while a
rich variety of non-trivial quantum phases could in principle also originate
from broken time-reversal symmetry, realizing systems that combine magnetism
with complex topological properties is remarkably elusive due to both
considerable experimental and theoretical challenges. Here, we demonstrate that
giant open Fermi arcs are created at the surface of ultrathin hybrid magnets.
The Fermi-surface topology of an atomically thin ferromagnet is substantially
modified by the hybridization with a heavy-metal substrate, giving rise to
Fermi-surface discontinuities that are bridged by the Fermi arcs. Due to the
interplay between magnetism and topology, we can control both the shape and the
location of the Fermi arcs by tuning the magnetization direction. The
hybridization points in the Fermi surface can be attributed to a non-trivial
"mixed" topology and induce hot spots in the Berry curvature, dominating spin
and charge transport as well as magneto-electric coupling effects.Comment: 14 pages, 10 figure
Provably Convergent Schr\"odinger Bridge with Applications to Probabilistic Time Series Imputation
The Schr\"odinger bridge problem (SBP) is gaining increasing attention in
generative modeling and showing promising potential even in comparison with the
score-based generative models (SGMs). SBP can be interpreted as an
entropy-regularized optimal transport problem, which conducts projections onto
every other marginal alternatingly. However, in practice, only approximated
projections are accessible and their convergence is not well understood. To
fill this gap, we present a first convergence analysis of the Schr\"odinger
bridge algorithm based on approximated projections. As for its practical
applications, we apply SBP to probabilistic time series imputation by
generating missing values conditioned on observed data. We show that optimizing
the transport cost improves the performance and the proposed algorithm achieves
the state-of-the-art result in healthcare and environmental data while
exhibiting the advantage of exploring both temporal and feature patterns in
probabilistic time series imputation.Comment: Accepted by ICML 202
Analysis of Y chromosome STR haplotypes in the European part of Russia reveals high diversities but non-significant genetic distances between populations
A total of 17 Y-specific STR loci were studied in 12 districts of the European part of Russia aiming to ascertain the amount of substructure required for the construction of a representative regional database. All groups exhibited high haplotype diversities but low inter-population variance as measured by an analysis of molecular variance. However, when Western Russia is taken as a whole, the genetic distances to the neighbouring populations were significant. Whereas gradual change in the Y chromosome pool exists between Russia and the Slavic-speaking populations to the West, remarkable discontinuities were observed with neighbouring populations in the East, North and South
Status of Muon Collider Research and Development and Future Plans
The status of the research on muon colliders is discussed and plans are
outlined for future theoretical and experimental studies. Besides continued
work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy
collider, many studies are now concentrating on a machine near 0.1 TeV (CoM)
that could be a factory for the s-channel production of Higgs particles. We
discuss the research on the various components in such muon colliders, starting
from the proton accelerator needed to generate pions from a heavy-Z target and
proceeding through the phase rotation and decay ()
channel, muon cooling, acceleration, storage in a collider ring and the
collider detector. We also present theoretical and experimental R & D plans for
the next several years that should lead to a better understanding of the design
and feasibility issues for all of the components. This report is an update of
the progress on the R & D since the Feasibility Study of Muon Colliders
presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A.
Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics
(Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].Comment: 95 pages, 75 figures. Submitted to Physical Review Special Topics,
Accelerators and Beam
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