Motivation: Single cell RNA sequencing (scRNA-seq) data makes studying the development of cells possible at unparalleled resolution. Given that many cellular differentiation processes are hierarchical, their scRNA-seq data is expected to be approximately tree-shaped in gene expression space. Inference and representation of this tree-structure in two dimensions is highly desirable for biological interpretation and exploratory analysis.Results:Our two contributions are an approach for identifying a meaningful tree structure from high-dimensional scRNA-seq data, and a visualization method respecting the tree-structure. We extract the tree structure by means of a density based minimum spanning tree on a vector quantization of the data and show that it captures biological information well. We then introduce DTAE, a tree-biased autoencoder that emphasizes the tree structure of the data in low dimensional space. We compare to other dimension reduction methods and demonstrate the success of our method both qualitatively and quantitatively on real and toy data.Availability: Our implementation relying on PyTorch and Higra is available at //github.com/hci-unihd/DTAE.
相關內容
Anomaly detection among a large number of processes arises in many applications ranging from dynamic spectrum access to cybersecurity. In such problems one can often obtain noisy observations aggregated from a chosen subset of processes that conforms to a tree structure. The distribution of these observations, based on which the presence of anomalies is detected, may be only partially known. This gives rise to the need for a search strategy designed to account for both the sample complexity and the detection accuracy, as well as cope with statistical models that are known only up to some missing parameters. In this work we propose a sequential search strategy using two variations of the Generalized Local Likelihood Ratio statistic. Our proposed Hierarchical Dynamic Search (HDS) strategy is shown to be order-optimal with respect to the size of the search space and asymptotically optimal with respect to the detection accuracy. An explicit upper bound on the error probability of HDS is established for the finite sample regime. Extensive experiments are conducted, demonstrating the performance gains of HDS over existing methods.
Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory of functional a posteriori error estimates, for which guaranteed upper bounds for the primal and dual variables and two-sided bounds for the primal-dual pair are obtained. We improve on the abstract results obtained with the functional approach by proposing four different ways of estimating the residual errors based on the extent the approximate solution has conservation properties, i.e.: (1) no conservation, (2) subdomain conservation, (3) grid-level conservation, and (4) exact conservation. This treatment results in sharper and fully computable estimates when mass is conserved either at the grid level or exactly, with a comparable structure to those obtained from grid-based a posteriori techniques. We demonstrate the practical effectiveness of our theoretical results through numerical experiments using four different discretization methods for synthetic problems and applications based on benchmarks of flow in fractured porous media.
The Bayesian information criterion (BIC), defined as the observed data log likelihood minus a penalty term based on the sample size $N$, is a popular model selection criterion for factor analysis with complete data. This definition has also been suggested for incomplete data. However, the penalty term based on the `complete' sample size $N$ is the same no matter whether in a complete or incomplete data case. For incomplete data, there are often only $N_i<N$ observations for variable $i$, which means that using the `complete' sample size $N$ implausibly ignores the amounts of missing information inherent in incomplete data. Given this observation, a novel criterion called hierarchical BIC (HBIC) for factor analysis with incomplete data is proposed. The novelty is that it only uses the actual amounts of observed information, namely $N_i$'s, in the penalty term. Theoretically, it is shown that HBIC is a large sample approximation of variational Bayesian (VB) lower bound, and BIC is a further approximation of HBIC, which means that HBIC shares the theoretical consistency of BIC. Experiments on synthetic and real data sets are conducted to access the finite sample performance of HBIC, BIC, and related criteria with various missing rates. The results show that HBIC and BIC perform similarly when the missing rate is small, but HBIC is more accurate when the missing rate is not small.
This paper describes an energy-preserving and globally time-reversible code for weakly compressible smoothed particle hydrodynamics (SPH). We do not add any additional dynamics to the Monaghan's original SPH scheme at the level of ordinary differential equation, but we show how to discretize the equations by using a corrected expression for density and by invoking a symplectic integrator. Moreover, to achieve the global-in-time reversibility, we have to correct the initial state, implement a conservative fluid-wall interaction, and use the fixed-point arithmetic. Although the numerical scheme is reversible globally in time (solvable backwards in time while recovering the initial conditions), we observe thermalization of the particle velocities and growth of the Boltzmann entropy. In other words, when we do not see all the possible details, as in the Boltzmann entropy, which depends only on the one-particle distribution function, we observe the emergence of the second law of thermodynamics (irreversible behavior) from purely reversible dynamics.
A High-dimensional and sparse (HiDS) matrix is frequently encountered in a big data-related application like an e-commerce system or a social network services system. To perform highly accurate representation learning on it is of great significance owing to the great desire of extracting latent knowledge and patterns from it. Latent factor analysis (LFA), which represents an HiDS matrix by learning the low-rank embeddings based on its observed entries only, is one of the most effective and efficient approaches to this issue. However, most existing LFA-based models perform such embeddings on a HiDS matrix directly without exploiting its hidden graph structures, thereby resulting in accuracy loss. To address this issue, this paper proposes a graph-incorporated latent factor analysis (GLFA) model. It adopts two-fold ideas: 1) a graph is constructed for identifying the hidden high-order interaction (HOI) among nodes described by an HiDS matrix, and 2) a recurrent LFA structure is carefully designed with the incorporation of HOI, thereby improving the representa-tion learning ability of a resultant model. Experimental results on three real-world datasets demonstrate that GLFA outperforms six state-of-the-art models in predicting the missing data of an HiDS matrix, which evidently supports its strong representation learning ability to HiDS data.
We introduce a novel methodology for particle filtering in dynamical systems where the evolution of the signal of interest is described by a SDE and observations are collected instantaneously at prescribed time instants. The new approach includes the discretisation of the SDE and the design of efficient particle filters for the resulting discrete-time state-space model. The discretisation scheme converges with weak order 1 and it is devised to create a sequential dependence structure along the coordinates of the discrete-time state vector. We introduce a class of space-sequential particle filters that exploits this structure to improve performance when the system dimension is large. This is numerically illustrated by a set of computer simulations for a stochastic Lorenz 96 system with additive noise. The new space-sequential particle filters attain approximately constant estimation errors as the dimension of the Lorenz 96 system is increased, with a computational cost that increases polynomially, rather than exponentially, with the system dimension. Besides the new numerical scheme and particle filters, we provide in this paper a general framework for discrete-time filtering in continuous-time dynamical systems described by a SDE and instantaneous observations. Provided that the SDE is discretised using a weakly-convergent scheme, we prove that the marginal posterior laws of the resulting discrete-time state-space model converge to the posterior marginal posterior laws of the original continuous-time state-space model under a suitably defined metric. This result is general and not restricted to the numerical scheme or particle filters specifically studied in this manuscript.
Email is one of the most widely used ways to communicate, with millions of people and businesses relying on it to communicate and share knowledge and information on a daily basis. Nevertheless, the rise in email users has occurred a dramatic increase in spam emails in recent years. Processing and managing emails properly for individuals and companies are getting increasingly difficult. This article proposes a novel technique for email spam detection that is based on a combination of convolutional neural networks, gated recurrent units, and attention mechanisms. During system training, the network is selectively focused on necessary parts of the email text. The usage of convolution layers to extract more meaningful, abstract, and generalizable features by hierarchical representation is the major contribution of this study. Additionally, this contribution incorporates cross-dataset evaluation, which enables the generation of more independent performance results from the model's training dataset. According to cross-dataset evaluation results, the proposed technique advances the results of the present attention-based techniques by utilizing temporal convolutions, which give us more flexible receptive field sizes are utilized. The suggested technique's findings are compared to those of state-of-the-art models and show that our approach outperforms them.
We develop methods for reducing the dimensionality of large data sets, common in biomedical applications. Learning about patients using genetic data often includes more features than observations, which makes direct supervised learning difficult. One method of reducing the feature space is to use latent Dirichlet allocation to group genetic variants in an unsupervised manner. Latent Dirichlet allocation describes a patient as a mixture of topics corresponding to genetic variants. This can be generalized as a Bayesian tensor decomposition to account for multiple feature variables. Our most significant contributions are with hierarchical topic modeling. We design distinct methods of incorporating hierarchical topic modeling, based on nested Chinese restaurant processes and Pachinko Allocation Machine, into Bayesian tensor decomposition. We apply these models to examine patients with one of four common types of cancer (breast, lung, prostate, and colorectal) and siblings with and without autism spectrum disorder. We linked the genes with their biological pathways and combine this information into a tensor of patients, counts of their genetic variants, and the genes' membership in pathways. We find that our trained models outperform baseline models, with respect to coherence, by up to 40%.
We propose a simple yet powerful extension of Bayesian Additive Regression Trees which we name Hierarchical Embedded BART (HE-BART). The model allows for random effects to be included at the terminal node level of a set of regression trees, making HE-BART a non-parametric alternative to mixed effects models which avoids the need for the user to specify the structure of the random effects in the model, whilst maintaining the prediction and uncertainty calibration properties of standard BART. Using simulated and real-world examples, we demonstrate that this new extension yields superior predictions for many of the standard mixed effects models' example data sets, and yet still provides consistent estimates of the random effect variances. In a future version of this paper, we outline its use in larger, more advanced data sets and structures.
We present a method for the control of robot swarms which allows the shaping and the translation of patterns of simple robots ("smart particles"), using two types of devices. These two types represent a hierarchy: a larger group of simple, oblivious robots (which we call the workers) that is governed by simple local attraction forces, and a smaller group (the guides) with sufficient mission knowledge to create and maintain a desired pattern by operating on the local forces of the former. This framework exploits the knowledge of the guides, which coordinate to shape the workers like smart particles by changing their interaction parameters. We study the approach with a large scale simulation experiment in a physics based simulator with up to 1000 robots forming three different patterns. Our experiments reveal that the approach scales well with increasing robot numbers, and presents little pattern distortion for a set of target moving shapes. We evaluate the approach on a physical swarm of robots that use visual inertial odometry to compute their relative positions and obtain results that are comparable with simulation. This work lays foundation for designing and coordinating configurable smart particles, with applications in smart materials and nanomedicine.
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