We consider the problem of transferring knowledge from a source, or proxy, domain to a new target domain for learning a high-dimensional regression model with possibly different features. Recently, the statistical properties of homogeneous transfer learning have been investigated. However, most homogeneous transfer and multi-task learning methods assume that the target and proxy domains have the same feature space, limiting their practical applicability. In applications, target and proxy feature spaces are frequently inherently different, for example, due to the inability to measure some variables in the target data-poor environments. Conversely, existing heterogeneous transfer learning methods do not provide statistical error guarantees, limiting their utility for scientific discovery. We propose a two-stage method that involves learning the relationship between the missing and observed features through a projection step in the proxy data and then solving a joint penalized regression optimization problem in the target data. We develop an upper bound on the method's parameter estimation risk and prediction risk, assuming that the proxy and the target domain parameters are sparsely different. Our results elucidate how estimation and prediction error depend on the complexity of the model, sample size, the extent of overlap, and correlation between matched and mismatched features.

Relationships among teachers are known to influence their teaching-related perceptions. We study whether and how teachers' advising relationships (networks) are related to their perceptions of satisfaction, students, and influence over educational policies, recorded as their responses to a questionnaire (item responses). We propose a novel joint model of network and item responses (JNIRM) with correlated latent variables to understand these co-varying ties. This methodology allows the analyst to test and interpret the dependence between a network and item responses. Using JNIRM, we discover that teachers' advising relationships contribute to their perceptions of satisfaction and students more often than their perceptions of influence over educational policies. In addition, we observe that the complementarity principle applies in certain schools, where teachers tend to seek advice from those who are different from them. JNIRM shows superior parameter estimation and model fit over separately modeling the network and item responses with latent variable models.

This paper aims to get a comprehensive review of current-day robotic computation technologies at VLSI architecture level. We studied several repots in the domain of robotic processor architecture. In this work, we focused on the forward kinematics architectures which consider CORDIC algorithms, VLSI circuits of WE DSP16 chip, parallel processing and pipelined architecture, and lookup table formula and FPGA processor. This study gives us an understanding of different implementation methods for forward kinematics. Our goal is to develop a forward kinematics processor with FPGA for real-time applications, requires a fast response time and low latency of these devices, useful for industrial automation where the processing speed plays a great role.

We investigate if there is a peer influence or role model effect on successful graduation from Therapeutic Communities (TCs). We analyze anonymized individual-level observational data from 3 TCs that kept records of written exchanges of affirmations and corrections among residents, and their precise entry and exit dates. The affirmations allow us to form peer networks, and the entry and exit dates allow us to define a causal effect of interest. We conceptualize the causal role model effect as measuring the difference in the expected outcome of a resident (ego) who can observe one of their social contacts (e.g., peers who gave affirmations), to be successful in graduating before the ego's exit vs not successfully graduating before the ego's exit. Since peer influence is usually confounded with unobserved homophily in observational data, we model the network with a latent variable model to estimate homophily and include it in the outcome equation. We provide a theoretical guarantee that the bias of our peer influence estimator decreases with sample size. Our results indicate there is an effect of peers' graduation on the graduation of residents. The magnitude of peer influence differs based on gender, race, and the definition of the role model effect. A counterfactual exercise quantifies the potential benefits of intervention of assigning a buddy to "at-risk" individuals directly on the treated resident and indirectly on their peers through network propagation.

Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models.

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks.

In many application settings involving networks, such as messages between users of an on-line social network or transactions between traders in financial markets, the observed data are in the form of relational events with timestamps, which form a continuous-time network. We propose the Community Hawkes Independent Pairs (CHIP) model for community detection on such timestamped relational event data. We demonstrate that applying spectral clustering to adjacency matrices constructed from relational events generated by the CHIP model provides consistent community detection for a growing number of nodes. In particular, we obtain explicit non-asymptotic upper bounds on the misclustering rates based on the separation conditions required on the parameters of the model for consistent community detection. We also develop consistent and computationally efficient estimators for the parameters of the model. We demonstrate that our proposed CHIP model and estimation procedure scales to large networks with tens of thousands of nodes and provides superior fits compared to existing continuous-time network models on several real networks.

Higher-order motif structures and multi-vertex interactions are becoming increasingly important in studies that aim to improve our understanding of functionalities and evolution patterns of networks. To elucidate the role of higher-order structures in community detection problems over complex networks, we introduce the notion of a Superimposed Stochastic Block Model (SupSBM). The model is based on a random graph framework in which certain higher-order structures or subgraphs are generated through an independent hyperedge generation process, and are then replaced with graphs that are superimposed with directed or undirected edges generated by an inhomogeneous random graph model. Consequently, the model introduces controlled dependencies between edges which allow for capturing more realistic network phenomena, namely strong local clustering in a sparse network, short average path length, and community structure. We proceed to rigorously analyze the performance of a number of recently proposed higher-order spectral clustering methods on the SupSBM. In particular, we prove non-asymptotic upper bounds on the misclustering error of spectral community detection for a SupSBM setting in which triangles or 3-uniform hyperedges are superimposed with undirected edges. As part of our analysis, we also derive new bounds on the misclustering error of higher-order spectral clustering methods for the standard SBM and the 3-uniform hypergraph SBM. Furthermore, for a non-uniform hypergraph SBM model in which one directly observes both edges and 3-uniform hyperedges, we obtain a criterion that describes when to perform spectral clustering based on edges and when on hyperedges, based on a function of hyperedge density and observation quality.

We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network or multiple snapshots of a time-varying network. Numerous methods have been proposed in the literature for the more general problem of multi-view clustering in the past decade based on the spectral clustering or a low-rank matrix factorization. As a general theme, these "intermediate fusion" methods involve obtaining a low column rank matrix by optimizing an objective function and then using the columns of the matrix for clustering. However, the theoretical properties of these methods remain largely unexplored and most researchers have relied on the performance in synthetic and real data to assess the goodness of the procedures. In the absence of statistical guarantees on the objective functions, it is difficult to determine if the algorithms optimizing the objective will return a good community structure. We apply some of these methods for consensus community detection in multi-layer networks and investigate the consistency properties of the global optimizer of the objective functions under the multi-layer stochastic blockmodel. We derive several new asymptotic results showing consistency of the intermediate fusion techniques along with the spectral clustering of mean adjacency matrix under a high dimensional setup, where the number of nodes, the number of layers and the number of communities of the multi-layer graph grow. Our numerical study shows that in comparison to the intermediate fusion techniques, late fusion methods, namely spectral clustering on aggregate spectral kernel and module allegiance matrix, under-perform in sparse networks, while the spectral clustering of mean adjacency matrix under-performs in multi-layer networks that contain layers with both homophilic and heterophilic clusters.

We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimization problem. We establish the connection of the factors obtained through the factorization to a non-negative basis of an invariant subspace of the estimated matrix, drawing parallel with the spectral clustering. Using such factorization for clustering in networks is motivated by analyzing a block-diagonal Laplacian matrix with the blocks representing the connected components of a graph. The method is shown to be consistent for community detection in graphs generated from the stochastic block model and the degree corrected stochastic block model. Simulation results and real data analysis show the effectiveness of these methods under a wide variety of situations, including sparse and highly heterogeneous graphs where the usual spectral clustering is known to fail. Our method also performs better than the state of the art in popular benchmark network datasets, e.g., the political web blogs and the karate club data.