Irregular Convolutional Neural Network (ICNN) 
Convolutional kernels are basic and vital components of deep Convolutional Neural Networks (CNN). In this paper, we equip convolutional kernels with shape attributes to generate the deep Irregular Convolutional Neural Networks (ICNN). Compared to traditional CNN applying regular convolutional kernels like ${3\times3}$, our approach trains irregular kernel shapes to better fit the geometric variations of input features. In other words, shapes are learnable parameters in addition to weights. The kernel shapes and weights are learned simultaneously during end-to-end training with the standard back-propagation algorithm. Experiments for semantic segmentation are implemented to validate the effectiveness of our proposed ICNN. …
HVARX
The Vector AutoRegressive (VAR) model is fundamental to the study of multivariate time series. Although VAR models are intensively investigated by many researchers, practitioners often show more interest in analyzing VARX models that incorporate the impact of unmodeled exogenous variables (X) into the VAR. However, since the parameter space grows quadratically with the number of time series, estimation quickly becomes challenging. While several proposals have been made to sparsely estimate large VAR models, the estimation of large VARX models is under-explored. Moreover, typically these sparse proposals involve a lasso-type penalty and do not incorporate lag selection into the estimation procedure. As a consequence, the resulting models may be difficult to interpret. In this paper, we propose a lag-based hierarchically sparse estimator, called ‘HVARX’, for large VARX models. We illustrate the usefulness of HVARX on a cross-category management marketing application. Our results show how it provides a highly interpretable model, and improves out-of-sample forecast accuracy compared to a lasso-type approach. …
Convolutional Analysis Operator Learning (CAOL)
Convolutional operator learning is increasingly gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called local approaches that extract and store many overlapping patches across training signals. Due to memory demands, local approaches have limitations when learning kernels from large datasets — particularly with multi-layered structures, e.g., convolutional neural network (CNN) — and/or applying the learned kernels to high-dimensional signal recovery problems. The so-called global approach has been studied within the ‘synthesis’ signal model, e.g., convolutional dictionary learning, overcoming the memory problems by careful algorithmic designs. This paper proposes a new convolutional analysis operator learning (CAOL) framework in the global approach, and develops a new convergent Block Proximal Gradient method using a Majorizer (BPG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame (TF) filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, for tight majorizers, BPG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art method, BPG. Numerical experiments for sparse-view computational tomography show that CAOL using TF filters significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Finally, this paper shows that CAOL can be useful to mathematically model a CNN, and the corresponding updates obtained via BPG-M coincide with core modules of the CNN. …
Like this:
Like Loading…
Related