Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within clusters, is mostly fixed in advance, in the recent literature models with automatic inference on both the number of clusters and latent factors have been introduced. The automatic inference is usually done by assigning a nonparametric prior and allowing the number of clusters and factors to potentially go to infinity. The MCMC estimation is performed via an adaptive algorithm, in which the parameters associated with the redundant factors are discarded as the chain moves. While this approach has clear advantages, it also bears some significant drawbacks. Running a separate factor-analytical model for each cluster involves matrices of changing dimensions, which can make the model and programming somewhat cumbersome. In addition, discarding the parameters associated with the redundant factors could lead to a bias in estimating cluster covariance matrices. At last, identification remains problematic for infinite factor models. The current work contributes to the MFA literature by providing for the automatic inference on the number of clusters and the number of cluster-specific factors while keeping both cluster and factor dimensions finite. This allows us to avoid many of the aforementioned drawbacks of the infinite models. For the automatic inference on the cluster structure, we employ the dynamic mixture of finite mixtures (MFM) model. Automatic inference on cluster-specific factors is performed by assigning an exchangeable shrinkage process (ESP) prior to the columns of the factor loading matrices. The performance of the model is demonstrated on several benchmark data sets as well as real data applications.
相關內容
Graph representations are the generalization of geometric graph drawings from the plane to higher dimensions. A method introduced by Tutte to optimize properties of graph drawings is to minimize their energy. We explore this minimization for spherical graph representations, where the vertices lie on a unit sphere such that the origin is their barycentre. We present a primal and dual semidefinite program which can be used to find such a spherical graph representation minimizing the energy. We denote the optimal value of this program by $\rho(G)$ for a given graph $G$. The value turns out to be related to the second largest eigenvalue of the adjacency matrix of $G$, which we denote by $\lambda_2$. We show that for $G$ regular, $\rho(G) \leq \frac{\lambda_{2}}{2} \cdot v(G)$, and that equality holds if and only if the $\lambda_{2}$ eigenspace contains a spherical 1-design. Moreover, if $G$ is a random $d$-regular graph, $\rho(G)=\left(\sqrt{(d-1)} +o(1)\right)\cdot v(G)$, asymptotically almost surely.
Training machine learning (ML) algorithms is a computationally intensive process, which is frequently memory-bound due to repeatedly accessing large training datasets. As a result, processor-centric systems (e.g., CPU, GPU) suffer from costly data movement between memory units and processing units, which consumes large amounts of energy and execution cycles. Memory-centric computing systems, i.e., with processing-in-memory (PIM) capabilities, can alleviate this data movement bottleneck. Our goal is to understand the potential of modern general-purpose PIM architectures to accelerate ML training. To do so, we (1) implement several representative classic ML algorithms (namely, linear regression, logistic regression, decision tree, K-Means clustering) on a real-world general-purpose PIM architecture, (2) rigorously evaluate and characterize them in terms of accuracy, performance and scaling, and (3) compare to their counterpart implementations on CPU and GPU. Our evaluation on a real memory-centric computing system with more than 2500 PIM cores shows that general-purpose PIM architectures can greatly accelerate memory-bound ML workloads, when the necessary operations and datatypes are natively supported by PIM hardware. For example, our PIM implementation of decision tree is $27\times$ faster than a state-of-the-art CPU version on an 8-core Intel Xeon, and $1.34\times$ faster than a state-of-the-art GPU version on an NVIDIA A100. Our K-Means clustering on PIM is $2.8\times$ and $3.2\times$ than state-of-the-art CPU and GPU versions, respectively. To our knowledge, our work is the first one to evaluate ML training on a real-world PIM architecture. We conclude with key observations, takeaways, and recommendations that can inspire users of ML workloads, programmers of PIM architectures, and hardware designers & architects of future memory-centric computing systems.
We investigate the complexity of several manipulation and control problems under numerous prevalent approval-based multiwinner voting rules. Particularly, the rules we study include approval voting (AV), satisfaction approval voting (SAV), net-satisfaction approval voting (NSAV), proportional approval voting (PAV), approval-based Chamberlin-Courant voting (ABCCV), minimax approval voting (MAV), etc. We show that these rules generally resist the strategic types scrutinized in the paper, with only a few exceptions. In addition, we also obtain many fixed-parameter tractability results for these problems with respect to several natural parameters, and derive polynomial-time algorithms for certain special cases.
We relate the power bound and a resolvent condition of Kreiss-Ritt type and characterize the extremal growth of two families of products of three Toeplitz operators on the Hardy space that contain infinitely many points in their spectra. Since these operators do not fall into a well-understood class, we analyze them through explicit techniques based on properties of Toeplitz operators and the structure of the Hardy space. Our methods apply mutatis mutandis to operators of the form $T_{g(z)}^{-1}T_{f(z)}T_{g(z)}$ where $f(z)$ is a polynomial in $z$ and $\bar{z}$ and $g(z)$ is a polynomial in $z$. This collection of operators arises in the numerical solution of the Cauchy problem for linear ordinary, partial, and delay differential equations that are frequently used as models for processes in the sciences and engineering. Our results provide a framework for the stability analysis of existing numerical methods for new classes of linear differential equations as well as the development of novel approximation schemes.
Despite decades of research, developing correct and scalable concurrent programs is still challenging. Network functions (NFs) are not an exception. This paper presents NFork, a system that helps NF domain experts to productively develop concurrent NFs by abstracting away concurrency from developers. The key scheme behind NFork's design is to exploit NF characteristics to overcome the limitations of prior work on concurrency programming. Developers write NFs as sequential programs, and during runtime, NFork performs transparent parallelization by processing packets in different cores. Exploiting NF characteristics, NFork leverages transactional memory and develops efficient concurrent data structures to achieve scalability and guarantee the absence of concurrency bugs. Since NFork manages concurrency, it further provides (i) a profiler that reveals the root causes of scalability bottlenecks inherent to the NF's semantics and (ii) actionable recipes for developers to mitigate these root causes by relaxing the NF's semantics. We show that NFs developed with NFork achieve competitive scalability with those in Cisco VPP [16], and NFork's profiler and recipes can effectively aid developers in optimizing NF scalability.
Deep Learning (DL) frameworks are now widely used, simplifying the creation of complex models as well as their integration to various applications even to non DL experts. However, like any other programs, they are prone to bugs. This paper deals with the subcategory of bugs named silent bugs: they lead to wrong behavior but they do not cause system crashes or hangs, nor show an error message to the user. Such bugs are even more dangerous in DL applications and frameworks due to the "black-box" and stochastic nature of the systems (the end user can not understand how the model makes decisions). This paper presents the first empirical study of Keras and TensorFlow silent bugs, and their impact on users' programs. We extracted closed issues related to Keras from the TensorFlow GitHub repository. Out of the 1,168 issues that we gathered, 77 were reproducible silent bugs affecting users' programs. We categorized the bugs based on the effects on the users' programs and the components where the issues occurred, using information from the issue reports. We then derived a threat level for each of the issues, based on the impact they had on the users' programs. To assess the relevance of identified categories and the impact scale, we conducted an online survey with 103 DL developers. The participants generally agreed with the significant impact of silent bugs in DL libraries and acknowledged our findings (i.e., categories of silent bugs and the proposed impact scale). Finally, leveraging our analysis, we provide a set of guidelines to facilitate safeguarding against such bugs in DL frameworks.
In the past decade, the deployment of deep learning (Artificial Intelligence (AI)) methods has become pervasive across a spectrum of real-world applications, often in safety-critical contexts. This comprehensive research article rigorously investigates the ethical dimensions intricately linked to the rapid evolution of AI technologies, with a particular focus on the healthcare domain. Delving deeply, it explores a multitude of facets including transparency, adept data management, human oversight, educational imperatives, and international collaboration within the realm of AI advancement. Central to this article is the proposition of a conscientious AI framework, meticulously crafted to accentuate values of transparency, equity, answerability, and a human-centric orientation. The second contribution of the article is the in-depth and thorough discussion of the limitations inherent to AI systems. It astutely identifies potential biases and the intricate challenges of navigating multifaceted contexts. Lastly, the article unequivocally accentuates the pressing need for globally standardized AI ethics principles and frameworks. Simultaneously, it aptly illustrates the adaptability of the ethical framework proposed herein, positioned skillfully to surmount emergent challenges.
Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering and recommendation systems, etc. According to the graph types, the existing KGR models can be roughly divided into three categories, \textit{i.e.,} static models, temporal models, and multi-modal models. The early works in this domain mainly focus on static KGR and tend to directly apply general knowledge graph embedding models to the reasoning task. However, these models are not suitable for more complex but practical tasks, such as inductive static KGR, temporal KGR, and multi-modal KGR. To this end, multiple works have been developed recently, but no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the preliminaries, summaries of KGR models, and typical datasets are introduced and discussed consequently. Moreover, we discuss the challenges and potential opportunities. The corresponding open-source repository is shared on GitHub: //github.com/LIANGKE23/Awesome-Knowledge-Graph-Reasoning.
This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.
Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require that a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with an arbitrary depth. Although the primitive graph neural networks have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on graph convolutional network (GCN) and gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191