Interpreting the learning dynamics of neural networks can provide useful insights into how networks learn and the development of better training and design approaches. We present an approach to interpret learning in neural networks by measuring relative weight change on a per layer basis and dynamically aggregating emerging trends through combination of dimensionality reduction and clustering which allows us to scale to very deep networks. We use this approach to investigate learning in the context of vision tasks across a variety of state-of-the-art networks and provide insights into the learning behavior of these networks, including how task complexity affects layer-wise learning in deeper layers of networks.

Optimization is often cast as a deterministic problem, where the solution is found through some iterative procedure such as gradient descent. However, when training neural networks the loss function changes over (iteration) time due to the randomized selection of a subset of the samples. This randomization turns the optimization problem into a stochastic one. We propose to consider the loss as a noisy observation with respect to some reference optimum. This interpretation of the loss allows us to adopt Kalman filtering as an optimizer, as its recursive formulation is designed to estimate unknown parameters from noisy measurements. Moreover, we show that the Kalman Filter dynamical model for the evolution of the unknown parameters can be used to capture the gradient dynamics of advanced methods such as Momentum and Adam. We call this stochastic optimization method KaFiStO. KaFiStO is an easy to implement, scalable, and efficient method to train neural networks. We show that it also yields parameter estimates that are on par with or better than existing optimization algorithms across several neural network architectures and machine learning tasks, such as computer vision and language modeling.

We establish an equivalence between the $\ell_2$-regularized solution path for a convex loss function, and the solution of an ordinary differentiable equation (ODE). Importantly, this equivalence reveals that the solution path can be viewed as the flow of a hybrid of gradient descent and Newton method applying to the empirical loss, which is similar to a widely used optimization technique called trust region method. This provides an interesting algorithmic view of $\ell_2$ regularization, and is in contrast to the conventional view that the $\ell_2$ regularization solution path is similar to the gradient flow of the empirical loss.New path-following algorithms based on homotopy methods and numerical ODE solvers are proposed to numerically approximate the solution path. In particular, we consider respectively Newton method and gradient descent method as the basis algorithm for the homotopy method, and establish their approximation error rates over the solution path. Importantly, our theory suggests novel schemes to choose grid points that guarantee an arbitrarily small suboptimality for the solution path. In terms of computational cost, we prove that in order to achieve an $\epsilon$-suboptimality for the entire solution path, the number of Newton steps required for the Newton method is $\mathcal O(\epsilon^{-1/2})$, while the number of gradient steps required for the gradient descent method is $\mathcal O\left(\epsilon^{-1} \ln(\epsilon^{-1})\right)$. Finally, we use $\ell_2$-regularized logistic regression as an illustrating example to demonstrate the effectiveness of the proposed path-following algorithms.

We present a new probabilistic model to address semi-nonnegative matrix factorization (SNMF), called Skellam-SNMF. It is a hierarchical generative model consisting of prior components, Skellam-distributed hidden variables and observed data. Two inference algorithms are derived: Expectation-Maximization (EM) algorithm for maximum \emph{a posteriori} estimation and Variational Bayes EM (VBEM) for full Bayesian inference, including the estimation of parameters prior distribution. From this Skellam-based model, we also introduce a new divergence $\mathcal{D}$ between a real-valued target data $x$ and two nonnegative parameters $\lambda_{0}$ and $\lambda_{1}$ such that $\mathcal{D}\left(x\mid\lambda_{0},\lambda_{1}\right)=0\Leftrightarrow x=\lambda_{0}-\lambda_{1}$, which is a generalization of the Kullback-Leibler (KL) divergence. Finally, we conduct experimental studies on those new algorithms in order to understand their behavior and prove that they can outperform the classic SNMF approach on real data in a task of automatic clustering.

We demonstrate the use of Adaptive Stress Testing to detect and address potential vulnerabilities in a financial environment. We develop a simplified model for credit card fraud detection that utilizes a linear regression classifier based on historical payment transaction data coupled with business rules. We then apply the reinforcement learning model known as Adaptive Stress Testing to train an agent, that can be thought of as a potential fraudster, to find the most likely path to system failure -- successfully defrauding the system. We show the connection between this most likely failure path and the limits of the classifier and discuss how the fraud detection system's business rules can be further augmented to mitigate these failure modes.

We study federated edge learning, where a global model is trained collaboratively using privacy-sensitive data at the edge of a wireless network. A parameter server (PS) keeps track of the global model and shares it with the wireless edge devices for training using their private local data. The devices then transmit their local model updates, which are used to update the global model, to the PS. The algorithm, which involves transmission over PS-to-device and device-to-PS links, continues until the convergence of the global model or lack of any participating devices. In this study, we consider device selection based on downlink channels over which the PS shares the global model with the devices. Performing digital downlink transmission, we design a partial device participation framework where a subset of the devices is selected for training at each iteration. Therefore, the participating devices can have a better estimate of the global model compared to the full device participation case which is due to the shared nature of the broadcast channel with the price of updating the global model with respect to a smaller set of data. At each iteration, the PS broadcasts different quantized global model updates to different participating devices based on the last global model estimates available at the devices. We investigate the best number of participating devices through experimental results for image classification using the MNIST dataset with biased distribution.

Attributed event sequences are commonly encountered in practice. A recent research line focuses on incorporating neural networks with the statistical model -- marked point processes, which is the conventional tool for dealing with attributed event sequences. Neural marked point processes possess good interpretability of probabilistic models as well as the representational power of neural networks. However, we find that performance of neural marked point processes is not always increasing as the network architecture becomes more complicated and larger, which is what we call the performance saturation phenomenon. This is due to the fact that the generalization error of neural marked point processes is determined by both the network representational ability and the model specification at the same time. Therefore we can draw two major conclusions: first, simple network structures can perform no worse than complicated ones for some cases; second, using a proper probabilistic assumption is as equally, if not more, important as improving the complexity of the network. Based on this observation, we propose a simple graph-based network structure called GCHP, which utilizes only graph convolutional layers, thus it can be easily accelerated by the parallel mechanism. We directly consider the distribution of interarrival times instead of imposing a specific assumption on the conditional intensity function, and propose to use a likelihood ratio loss with a moment matching mechanism for optimization and model selection. Experimental results show that GCHP can significantly reduce training time and the likelihood ratio loss with interarrival time probability assumptions can greatly improve the model performance.

Assigning meaning to parts of image data is the goal of semantic image segmentation. Machine learning methods, specifically supervised learning is commonly used in a variety of tasks formulated as semantic segmentation. One of the major challenges in the supervised learning approaches is expressing and collecting the rich knowledge that experts have with respect to the meaning present in the image data. Towards this, typically a fixed set of labels is specified and experts are tasked with annotating the pixels, patches or segments in the images with the given labels. In general, however, the set of classes does not fully capture the rich semantic information present in the images. For example, in medical imaging such as histology images, the different parts of cells could be grouped and sub-grouped based on the expertise of the pathologist. To achieve such a precise semantic representation of the concepts in the image, we need access to the full depth of knowledge of the annotator. In this work, we develop a novel approach to collect segmentation annotations from experts based on psychometric testing. Our method consists of the psychometric testing procedure, active query selection, query enhancement, and a deep metric learning model to achieve a patch-level image embedding that allows for semantic segmentation of images. We show the merits of our method with evaluation on the synthetically generated image, aerial image and histology image.

Contextual bandits are a rich model for sequential decision making given side information, with important applications, e.g., in recommender systems. We propose novel algorithms for contextual bandits harnessing neural networks to approximate the unknown reward function. We resolve the open problem of proving sublinear regret bounds in this setting for general context sequences, considering both fully-connected and convolutional networks. To this end, we first analyze NTK-UCB, a kernelized bandit optimization algorithm employing the Neural Tangent Kernel (NTK), and bound its regret in terms of the NTK maximum information gain $\gamma_T$, a complexity parameter capturing the difficulty of learning. Our bounds on $\gamma_T$ for the NTK may be of independent interest. We then introduce our neural network based algorithm NN-UCB, and show that its regret closely tracks that of NTK-UCB. Under broad non-parametric assumptions about the reward function, our approach converges to the optimal policy at a $\tilde{\mathcal{O}}(T^{-1/2d})$ rate, where $d$ is the dimension of the context.

In this paper, we propose deep architectures for learning instance specific abstain (reject option) binary classifiers. The proposed approach uses double sigmoid loss function as described by Kulin Shah and Naresh Manwani in ("Online Active Learning of Reject Option Classifiers", AAAI, 2020), as a performance measure. We show that the double sigmoid loss is classification calibrated. We also show that the excess risk of 0-d-1 loss is upper bounded by the excess risk of double sigmoid loss. We derive the generalization error bounds for the proposed architecture for reject option classifiers. To show the effectiveness of the proposed approach, we experiment with several real world datasets. We observe that the proposed approach not only performs comparable to the state-of-the-art approaches, it is also robust against label noise. We also provide visualizations to observe the important features learned by the network corresponding to the abstaining decision.