Summary Network latent space models assume that each node is associated with an unobserved latent position in a Euclidean space, and such latent variables determine the probability of two nodes connecting with each other. In many applications, nodes in the network are often observed along with high-dimensional node variables, and these node variables provide important information for understanding the network structure. However, classical network latent space models have several limitations in incorporating node variables. In this paper, we propose a joint latent space model where we assume that the latent variables not only explain the network structure, but are also informative for the multivariate node variables. We develop a projected gradient descent algorithm that estimates the latent positions using a criterion incorporating both network structure and node variables. We establish theoretical properties of the estimators and provide insights into how incorporating high-dimensional node variables could improve the estimation accuracy of the latent positions. We demonstrate the improvement in latent variable estimation and the improvements in associated downstream tasks, such as missing value imputation for node variables, by simulation studies and an application to a Facebook data example.
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Disentangling ferroelectric domain wall geometries and pathways in dynamic piezoresponse force microscopy via unsupervised machine learning
Abstract Domain switching pathways in ferroelectric materials visualized by dynamic piezoresponse force microscopy (PFM) are explored via variational autoencoder, which simplifies the elements of the observed domain structure, crucially allowing for rotational invariance, thereby reducing the variability of local polarization distributions to a small number of latent variables. For small sampling window sizes the latent space is degenerate, and variability is observed only in the direction of a single latent variable that can be identified with the presence of domain wall. For larger window sizes, the latent space is 2D, and the disentangled latent variables can be generally interpreted as the degree of switching and complexity of domain structure. Applied to multiple consecutive PFM images acquired while monitoring domain switching, the polarization switching mechanism can thus be visualized in the latent space, providing insight into domain evolution mechanisms and their correlation with the microstructure.
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- Award ID(s):
- 1726862
- NSF-PAR ID:
- 10315569
- Date Published:
- Journal Name:
- Nanotechnology
- Volume:
- 33
- Issue:
- 5
- ISSN:
- 0957-4484
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Domain adaptation is an important but challenging task. Most of the existing domain adaptation methods struggle to extract the domain-invariant representation on the feature space with entangling domain information and semantic information. Different from previous efforts on the entangled feature space, we aim to extract the domain invariant semantic information in the latent disentangled semantic representation (DSR) of the data. In DSR, we assume the data generation process is controlled by two independent sets of variables, i.e., the semantic latent variables and the domain latent variables. Under the above assumption, we employ a variational auto-encoder to reconstruct the semantic latent variables and domain latent variables behind the data. We further devise a dual adversarial network to disentangle these two sets of reconstructed latent variables. The disentangled semantic latent variables are finally adapted across the domains. Experimental studies testify that our model yields state-of-the-art performance on several domain adaptation benchmark datasets.
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Abstract Functional characterization of antiferroelectric (AFE) materials typically involves macroscopic testing of their nonlocal integrated information on their dielectric properties, such as polarization hysteresis loops, field‐dependent strain, and capacitance while the local AFE properties have been rarely addressed. Here, a new protocol is demonstrated for local probing of the antiferroelectric/ferroelectric (AFE/FE) phase transition in PbZrO3capacitors by piezoresponse force microscopy (PFM). PFM spectroscopy of the local AFE/FE phase transition parameters is performed and their spatial variability via two‐dimensional mapping is investigated. It is shown that AFE hysteresis loops recorded by PFM in the bias‐on regime exhibit four characteristic amplitude peaks. Within the framework of Landau theory, these features are attributed to a considerable increase in the electromechanical strain response due to the dielectric constant divergence during AFE/FE phase transitions. The proposed approach can be used to differentiate between the antiferroelectric and nonpolar dielectric phases in functional devices using the electrically induced polarization.
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Abstract One of the general features of ferroelectric systems is a complex nature of polarization reversal, which involves domain nucleation and motion of domain walls. Here, time‐resolved nanoscale domain imaging is applied in conjunction with the integral switching current measurements to investigate the mechanism of polarization reversal in yttrium‐doped HfO2(Y:HfO2)—currently one of the most actively studied ferroelectric systems. More specifically, the effect of film microstructure on the nucleation process is investigated by performing a comparative study of the polarization switching behavior in the epitaxial and polycrystalline Y:HfO2thin film capacitors. It is found that although the epitaxial Y:HfO2capacitors tend to switch slower than their polycrystalline counterparts, they exhibit a significantly higher nucleation density and rate, suggesting that this is a rate‐limiting mechanism. In addition, it is observed that under the external fields approaching the activation field value, the switching kinetics can be described equally well by the nucleation limited switching and the Kolmogorov‐Avrami‐Ishibashi models for both types of capacitors. This signifies convergence of two different mechanisms implying that the polarization reversal proceeds via a homogeneous nucleation process unaffected by the film microstructure, which can be considered as approaching the intrinsic switching limit.
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Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of both causal structure and latent variables can be achieved under mild assumptions: on causal structures, we allow for the existence of multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we do not make parametric assumptions, thus permitting general nonlinearity and multi-dimensional continuous variables. Specifically, we first develop a basic identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-6528/ac2f5b
