We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

The Web of Human Sexual Contacts

2004아테네 올림픽대회출전 한국레슬링 대표선수의 무산소성 운동능력 및 등속성 근력

The broad application of artificial intelligence techniques in medicine is currently hindered by limited dataset availability for algorithm training and validation, due to the absence of standardized electronic medical records, and strict legal and ethical requirements to protect patient privacy. In medical imaging, harmonized data exchange formats such as Digital Imaging and Communication in Medicine and electronic data storage are the standard, partially addressing the first issue, but the requirements for privacy preservation are equally strict. To prevent patient privacy compromise while promoting scientific research on large datasets that aims to improve patient care, the implementation of technical solutions to simultaneously address the demands for data protection and utilization is mandatory. Here we present an overview of current and next-generation methods for federated, secure and privacy-preserving artificial intelligence with a focus on medical imaging applications, alongside potential attack vectors and future prospects in medical imaging and beyond. Medical imaging data is often subject to privacy and intellectual property restrictions. AI techniques can help out by offering tools like federated learning to bridge the gap between personal data protection and data utilisation for research and clinical routine, but these tools need to be secure.

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Secure, privacy-preserving and federated machine learning in medical imaging

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وضعیت برونداد علمی دانشگاه علوم پزشکی کردستان براساس شاخصهای علم سنجی تا پایان سال 2011 میلادی

We design and implement a scalable version of loopy belief propagation (BP), a widely used algorithm for performing inference on probabilistic graphical models. However, implementations of BP on generic data processing platforms such as Apache Spark do not scale well to very large graphical models containing billions of vertices. To handle such large-scale graphs, we leverage a number of strategies. Our implementation is based on Apache Spark GraphX. We propose a novel graph partitioning strategy to reduce both computation and communication overhead providing a 2x speed-up. We use efficient memory management for storing the graph and shared memory for highspeed communication. To evaluate performance and demonstrate scalability of the approach, we perform a range of experiments including using real-world graphs with billions of vertices, where we achieve an overall 10x speed-up over a vanilla Spark baseline. Further, we apply our BP implementation to infer the probability of a website being malicious by performing inference on a graphical model derived from real, large-scale hyperlinked webcrawl data. We have open sourced our implementation.

Sandpiper: Scaling probabilistic inferencing to large scale graphical models

Many applications today, such as NLP, network analysis, and code analysis, rely on semantically embedding objects into low-dimensional fixed-length vectors. Such embeddings naturally provide a way to perform useful downstream tasks, such as identifying relations among objects or predicting objects for a given context, etc. Unfortunately, the training necessary for accurate embeddings is usually computationally intensive and requires processing large amounts of data. Furthermore, distributing this training is challenging. Most embedding training uses stochastic gradient descent (SGD), an "inherently" sequential algorithm. Prior approaches to parallelizing SGD do not honor these dependencies and thus potentially suffer poor convergence. 
This paper presents a distributed training framework for a class of applications that use Skip-gram-like models to generate embeddings. We call this class Any2Vec and it includes Word2Vec, DeepWalk, and Node2Vec among others. We first formulate Any2Vec training algorithm as a graph application and leverage the state-of-the-art distributed graph analytics framework, D-Galois. We adapt D-Galois to support dynamic graph generation and repartitioning, and incorporate novel communication optimizations. Finally, we introduce a novel way to combine gradients during distributed training to prevent accuracy loss. We show that our framework, called GraphAny2Vec, matches on a cluster of 32 hosts the accuracy of the state-of-the-art shared-memory implementations of Word2Vec and Vertex2Vec on 1 host, and gives a geo-mean speedup of 12x and 5x respectively. Furthermore, GraphAny2Vec is on average 2x faster than the state-of-the-art distributed Word2Vec implementation, DMTK, on 32 hosts. We also show the superiority of our Gradient Combiner independent of GraphAny2Vec by incorporating it in DMTK, which raises its accuracy by > 30%.

Distributed Training of Embeddings using Graph Analytics

Word embeddings capture semantic and syntactic similarities of words, represented as vectors. Word2Vec is a popular implementation of word embeddings; it takes as input a large corpus of text and learns a model that maps unique words in that corpus to other contextually relevant words. After training, Word2Vec's internal vector representation of words in the corpus map unique words to a vector space, which are then used in many downstream tasks. Training these models requires significant computational resources (training time often measured in days) and is difficult to parallelize. Most word embedding training uses stochastic gradient descent (SGD), an "inherently" sequential algorithm where at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing SGD do not honor these dependencies and thus potentially suffer poor convergence. This paper introduces GraphWord2Vec, a distributedWord2Vec algorithm which formulates the Word2Vec training process as a distributed graph problem and thus leverage state-of-the-art distributed graph analytics frameworks such as D-Galois and Gemini that scale to large distributed clusters. GraphWord2Vec also demonstrates how to use model combiners to honor data dependencies in SGD and thus scale without giving up convergence. We will show that GraphWord2Vec has linear scalability up to 32 machines converging as fast as a sequential run in terms of epochs, thus reducing training time by 14x.

Distributed Word2Vec using Graph Analytics Frameworks.

Graph transformer networks (GTN) are a variant of graph convolutional networks (GCN) that are targeted to heterogeneous graphs in which nodes and edges have associated type information that can be exploited to improve inference accuracy. GTNs learn important metapaths in the graph, create weighted edges for these metapaths, and use the resulting graph in a GCN. Currently, the only available implementation of GTNs uses dense matrix multiplication to find metapaths. Unfortunately, the space overhead of this approach can be large, so in practice it is used only for small graphs. In addition, the matrix-based implementation is not fine-grained enough to use random-walk based methods to optimize metapath finding. In this paper, we present a graph-based formulation and implementation of the GTN metapath finding problem. This graph-based formulation has two advantages over the matrix-based approach. First, it is more space efficient than the original GTN implementation and more compute-efficient for metapath sizes of practical interest. Second, it permits us to implement a sampling method that reduces the number of metapaths that must be enumerated, allowing the implementation to be used for larger graphs and larger metapath sizes. Experimental results show that our implementation is $6.5\times$ faster than the original GTN implementation on average for a metapath length of 4, and our sampling implementation is $155\times$ faster on average than this implementation without compromising on the accuracy of the GTN.

Optimizing Graph Transformer Networks with Graph-based Techniques.

Embodiments provide for optimizing the generation, evaluation, and selection of tensor circuit specifications for a tensor circuit to perform homomorphic encryption operations on encrypted data. A computing device having an improved compiler and runtime configuration can obtain a tensor circuit and associated schema. The computing device can map the obtained tensor circuit to an equivalent tensor circuit, adapted to perform fully homomorphic encryption (FHE) operations, and instantiated based on the obtained associated scheme. The computing device can then monitor a flow of data through the equivalent FHE-adapted tensor circuit utilizing various tensor circuit specifications determined therefor. A cost of each tensor circuit specification can be determined by the computing device based on the monitored flow of data, so as to identify an optimal set of optimal tensor circuit specifications that can be employed by the obtained tensor circuit, to efficiently perform homomorphic encryption operations on encrypted data.

Roshan Dathathri

Papers

Sandpiper: Scaling probabilistic inferencing to large scale graphical models

Distributed Training of Embeddings using Graph Analytics

Distributed Word2Vec using Graph Analytics Frameworks.

Optimizing Graph Transformer Networks with Graph-based Techniques.

Homomorphic evaluation of tensor programs