534 research outputs found
Simulation of stochastic Volterra equations driven by space--time L\'evy noise
In this paper we investigate two numerical schemes for the simulation of
stochastic Volterra equations driven by space--time L\'evy noise of pure-jump
type. The first one is based on truncating the small jumps of the noise, while
the second one relies on series representation techniques for infinitely
divisible random variables. Under reasonable assumptions, we prove for both
methods - and almost sure convergence of the approximations to the true
solution of the Volterra equation. We give explicit convergence rates in terms
of the Volterra kernel and the characteristics of the noise. A simulation study
visualizes the most important path properties of the investigated processes
Importance sampling of heavy-tailed iterated random functions
We consider a stochastic recurrence equation of the form , where ,
and is an i.i.d. sequence of positive random
vectors. The stationary distribution of this Markov chain can be represented as
the distribution of the random variable . Such random variables can be found in the analysis of
probabilistic algorithms or financial mathematics, where would be called a
stochastic perpetuity. If one interprets as the interest rate at
time , then is the present value of a bond that generates unit of
money at each time point . We are interested in estimating the probability
of the rare event , when is large; we provide a consistent
simulation estimator using state-dependent importance sampling for the case,
where is heavy-tailed and the so-called Cram\'{e}r condition is not
satisfied. Our algorithm leads to an estimator for . We show that under
natural conditions, our estimator is strongly efficient. Furthermore, we extend
our method to the case, where is defined via the
recursive formula and
is a sequence of i.i.d. random Lipschitz functions
Attenuated Responses To Inflammatory Cytokines In Mouse Embryonic Stem Cells: Biological Implications And The Molecular Basis
Embryonic stem cells (ESCs) have attracted intense interest due to their great potential for regenerative medicine. However, their immune property is an overlooked but a significant issue that needs to be thoroughly investigated not only to resolve the concern for therapeutic applications but also for further understanding the early stage of organismal development. Recent studies demonstrated that ESCs are deficient in innate immune responses to viral/bacterial infections and inflammatory cytokines. Inflammatory conditions generally inhibit cell proliferation, which could be detrimental to ESCs, since cell proliferation is their dedicated task during early embryogenesis. Thus, I hypothesize that the attenuated innate immunity in ESCs could allow them to evade the cytotoxicity caused by immune reactions and is, therefore, a self-protective mechanism during early embryogenesis. We have differentiated mouse ESCs (mESCs) to fibroblast-like cells (mESC-FBs) which were proved to have partially developed innate immunity. Using these cells as a model for comparison with mESCs, the insensitivity of mESCs to the cytotoxic effects from IFNg, which is an inflammatory cytokine highly presented during early embryogenesis, and other inflammatory conditions were demonstrated, including attenuated expressions of inflammatory and signaling molecules, inactivated transcription factor and unaffected cell viability. Furthermore, basal expressions of protein phosphatases that inhibit IFNg pathway were higher in mESCs than mESC-FBs. Treating mESCs with protein phosphatases inhibitor upregulated the expression of IFNg induced signaling molecule. In all, the attenuated inflammatory responses are beneficial for mESCs, and the inhibition effects from protein phosphatases could, at least, partially explain their attenuated responses to IFNg
Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes
We propose a class of strongly efficient rare event simulation estimators for
random walks and compound Poisson processes with a regularly varying
increment/jump-size distribution in a general large deviations regime. Our
estimator is based on an importance sampling strategy that hinges on the
heavy-tailed sample path large deviations result recently established in Rhee,
Blanchet, and Zwart (2016). The new estimators are straightforward to implement
and can be used to systematically evaluate the probability of a wide range of
rare events with bounded relative error. They are "universal" in the sense that
a single importance sampling scheme applies to a very general class of rare
events that arise in heavy-tailed systems. In particular, our estimators can
deal with rare events that are caused by multiple big jumps (therefore, beyond
the usual principle of a single big jump) as well as multidimensional processes
such as the buffer content process of a queueing network. We illustrate the
versatility of our approach with several applications that arise in the context
of mathematical finance, actuarial science, and queueing theory
AutoKG: Efficient Automated Knowledge Graph Generation for Language Models
Traditional methods of linking large language models (LLMs) to knowledge
bases via the semantic similarity search often fall short of capturing complex
relational dynamics. To address these limitations, we introduce AutoKG, a
lightweight and efficient approach for automated knowledge graph (KG)
construction. For a given knowledge base consisting of text blocks, AutoKG
first extracts keywords using a LLM and then evaluates the relationship weight
between each pair of keywords using graph Laplace learning. We employ a hybrid
search scheme combining vector similarity and graph-based associations to
enrich LLM responses. Preliminary experiments demonstrate that AutoKG offers a
more comprehensive and interconnected knowledge retrieval mechanism compared to
the semantic similarity search, thereby enhancing the capabilities of LLMs in
generating more insightful and relevant outputs.Comment: 10 pages, accepted by IEEE BigData 2023 as a workshop paper in GTA
Learning hypergraphs from signals with dual smoothness prior
Hypergraph structure learning, which aims to learn the hypergraph structures from the observed signals to capture the intrinsic high-order relationships among the entities, becomes crucial when a hypergraph topology is not readily available in the datasets. There are two challenges that lie at the heart of this problem: 1) how to handle the huge search space of potential hyperedges, and 2) how to define meaningful criteria to measure the relationship between the signals observed on nodes and the hypergraph structure. In this paper, for the first challenge, we adopt the assumption that the ideal hypergraph structure can be derived from a learnable graph structure that captures the pairwise relations within signals. Further, we propose a hypergraph structure learning framework HGSL with a novel dual smoothness prior that reveals a mapping between the observed node signals and the hypergraph structure, whereby each hyperedge corresponds to a subgraph with both node signal smoothness and edge signal smoothness in the learnable graph structure. Finally, we conduct extensive experiments to evaluate HGSL on both synthetic and real world datasets. Experiments show that HGSL can efficiently infer meaningful hypergraph topologies from observed signals
Hypergraph Structure Inference From Data Under Smoothness Prior
Hypergraphs are important for processing data with higher-order relationships
involving more than two entities. In scenarios where explicit hypergraphs are
not readily available, it is desirable to infer a meaningful hypergraph
structure from the node features to capture the intrinsic relations within the
data. However, existing methods either adopt simple pre-defined rules that fail
to precisely capture the distribution of the potential hypergraph structure, or
learn a mapping between hypergraph structures and node features but require a
large amount of labelled data, i.e., pre-existing hypergraph structures, for
training. Both restrict their applications in practical scenarios. To fill this
gap, we propose a novel smoothness prior that enables us to design a method to
infer the probability for each potential hyperedge without labelled data as
supervision. The proposed prior indicates features of nodes in a hyperedge are
highly correlated by the features of the hyperedge containing them. We use this
prior to derive the relation between the hypergraph structure and the node
features via probabilistic modelling. This allows us to develop an unsupervised
inference method to estimate the probability for each potential hyperedge via
solving an optimisation problem that has an analytical solution. Experiments on
both synthetic and real-world data demonstrate that our method can learn
meaningful hypergraph structures from data more efficiently than existing
hypergraph structure inference methods
Learning Hypergraphs From Signals With Dual Smoothness Prior
The construction of a meaningful hypergraph topology is the key to processing
signals with high-order relationships that involve more than two entities.
Learning the hypergraph structure from the observed signals to capture the
intrinsic relationships among the entities becomes crucial when a hypergraph
topology is not readily available in the datasets. There are two challenges
that lie at the heart of this problem: 1) how to handle the huge search space
of potential hyperedges, and 2) how to define meaningful criteria to measure
the relationship between the signals observed on nodes and the hypergraph
structure. In this paper, to address the first challenge, we adopt the
assumption that the ideal hypergraph structure can be derived from a learnable
graph structure that captures the pairwise relations within signals. Further,
we propose a hypergraph learning framework with a novel dual smoothness prior
that reveals a mapping between the observed node signals and the hypergraph
structure, whereby each hyperedge corresponds to a subgraph with both node
signal smoothness and edge signal smoothness in the learnable graph structure.
Finally, we conduct extensive experiments to evaluate the proposed framework on
both synthetic and real world datasets. Experiments show that our proposed
framework can efficiently infer meaningful hypergraph topologies from observed
signals.Comment: We have polished the paper and fixed some typos and the correct
number of the target hyperedges is given to the baseline in this versio
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