A traditional artificial neural network (ANN) is normally trained slowly by a gradient descent algorithm, such as the backpropagation algorithm, since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. Since a large number of hyperparameters of a deep neural network, such as a convolutional neural network, occupy much memory, a memory-inefficient deep learning model is not ideal for real-time Internet of Things (IoT) applications on various devices, such as mobile phones. Thus, it is necessary to develop fast and memory-efficient Artificial Intelligence of Things (AIoT) systems for real-time on-device applications. We created a novel wide and shallow 4-layer ANN called "Pairwise Neural Network" ("PairNet") with high-speed non-gradient-descent hyperparameter optimization. The PairNet is trained quickly with only one epoch since its hyperparameters are directly optimized one-time via simply solving a system of linear equations by using the multivariate least squares fitting method. In addition, an n-input space is partitioned into many n-input data subspaces, and a local PairNet is built in a local n-input subspace. This divide-and-conquer approach can train the local PairNet using specific local features to improve model performance. Simulation results indicate that the three PairNets with incremental learning have smaller average prediction mean squared errors, and achieve much higher speeds than traditional ANNs. An important future work is to develop better and faster non-gradient-descent hyperparameter optimization algorithms to generate effective, fast, and memory-efficient PairNets with incremental learning on optimal subspaces for real-time AIoT on-device applications.

In the constrained continuous optimization, barrier functions are usually used to impose an increasingly large cost on a feasible point as it approaches the boundary of the feasible region [32]. In effect, barrier functions replace constraints by a penalizing term in the primal objective function so that the solution stays away from the boundary of the feasible region. This is an attempt to approximate a constrained optimization problem with an unconstrained one and to later apply standard optimization techniques. While the benefits of barrier functions are studied extensively in the continuous domain [32], their use in discrete optimization is not very well understood. In this paper, we show how discrete barrier functions manifest themselves in constrained submodular maximization. Submodular functions formalize the intuitive diminishing returns condition, a property that not only allows optimization tractability but also appears in many machine learning applications, including video, image, and text summarization [7, 12, 23, 28, 35], active set selection in nonparametric learning [26], sequential decision making [27, 29] sensor placement, information gathering [10], privacy and fairness [16].

In this paper, we propose a new RWO-Sampling (Random Walk Over-Sampling) based on graphs for imbalanced datasets. In this method, two figures based on under-sampling and over-sampling methods are introduced to keep the proximity information, which is robust to noises and outliers. After the construction of the first graph on minority class, RWO-Sampling will be implemented on selected samples, and the rest of them will remain unchanged. The second graph is constructed for the majority class, and the samples in a low-density area (outliers) are removed. In the proposed method, examples of the majority class in a high-density area are selected, and the rest of them are eliminated. Furthermore, utilizing RWO-sampling, the boundary of minority class is increased though, the outliers are not raised. This method is tested, and the number of evaluation measures is compared to previous methods on nine continuous attribute datasets with different over-sampling rates. The experimental results were an indicator of the high efficiency and flexibility of the proposed method for the classification of imbalanced data.

In this paper, we propose scalable methods for maximizing a regularized submodular function $f = g - \ell$ expressed as the difference between a monotone submodular function $g$ and a modular function $\ell$. Indeed, submodularity is inherently related to the notions of diversity, coverage, and representativeness. In particular, finding the mode of many popular probabilistic models of diversity, such as determinantal point processes, submodular probabilistic models, and strongly log-concave distributions, involves maximization of (regularized) submodular functions. Since a regularized function $f$ can potentially take on negative values, the classic theory of submodular maximization, which heavily relies on the non-negativity assumption of submodular functions, may not be applicable. To circumvent this challenge, we develop the first one-pass streaming algorithm for maximizing a regularized submodular function subject to a $k$-cardinality constraint. It returns a solution $S$ with the guarantee that $f(S)\geq(\phi^{-2}-\epsilon) \cdot g(OPT)-\ell (OPT)$, where $\phi$ is the golden ratio. Furthermore, we develop the first distributed algorithm that returns a solution $S$ with the guarantee that $\mathbb{E}[f(S)] \geq (1-\epsilon) [(1-e^{-1}) \cdot g(OPT)-\ell(OPT)]$ in $O(1/ \epsilon)$ rounds of MapReduce computation, without keeping multiple copies of the entire dataset in each round (as it is usually done). We should highlight that our result, even for the unregularized case where the modular term $\ell$ is zero, improves the memory and communication complexity of the existing work by a factor of $O(1/ \epsilon)$ while arguably provides a simpler distributed algorithm and a unifying analysis. We also empirically study the performance of our scalable methods on a set of real-life applications, including finding the mode of distributions, data summarization, and product recommendation.

GPs are designed through parametrizing a covariance kernel, meaning that constructing expressive kernels allows for an improved representation of complex signals. Recent advances extend the GP concept to multiple series (or channels), where both auto-correlations and cross-correlations among channels are designed jointly; we refer to these models as multi-output GP (MOGP) models. A key attribute of MOGPs is that appropriate cross-correlations allow for improved data-imputation and prediction tasks when the channels have missing data. Popular MOGP models include: i) the Linear Model of Coregionalization (LMC) [2], ii) the Cross-Spectral Mixture (CSM) [3], iii) the Convolutional Model (CONV) [4], and iv) the Multi-Output Spectral Mixture (MOSM) [5]. Training MOGPs is challenging due to the large number of parameters required to model all the cross-correlations, and the fact that most of MOGP models are parametrized in the spectral domain, thus being prone to local minima. Therefore, a unified framework that implements these MOGPs is required both by the the GP research community as well as by those interested in practical applications for multi-channel data.

The curse of dimensionality is a critical challenge in Bayesian inference for high dimensional parameters. In this work, we address this challenge by developing a projected Stein variational gradient descent (pSVGD) method, which projects the parameters into a subspace that is adaptively constructed using the gradient of the log-likelihood, and applies SVGD for the much lower-dimensional coefficients of the projection. We provide an upper bound for the projection error with respect to the posterior and demonstrate the accuracy (compared to SVGD) and scalability of pSVGD with respect to the number of parameters, samples, data points, and processor cores.

The 01 loss is robust to outliers and tolerant to noisy data compared to convex loss functions. We conjecture that the 01 loss may also be more robust to adversarial attacks. To study this empirically we have developed a stochastic coordinate descent algorithm for a linear 01 loss classifier and a single hidden layer 01 loss neural network. Due to the absence of the gradient we iteratively update coordinates on random subsets of the data for fixed epochs. We show our algorithms to be fast and comparable in accuracy to the linear support vector machine and logistic loss single hidden layer network for binary classification on several image benchmarks, thus establishing that our method is on-par in test accuracy with convex losses. We then subject them to accurately trained substitute model black box attacks on the same image benchmarks and find them to be more robust than convex counterparts. On CIFAR10 binary classification task between classes 0 and 1 with adversarial perturbation of 0.0625 we see that the MLP01 network loses 27\% in accuracy whereas the MLP-logistic counterpart loses 83\%. Similarly on STL10 and ImageNet binary classification between classes 0 and 1 the MLP01 network loses 21\% and 20\% while MLP-logistic loses 67\% and 45\% respectively. On MNIST that is a well-separable dataset we find MLP01 comparable to MLP-logistic and show under simulation how and why our 01 loss solver is less robust there. We then propose adversarial training for our linear 01 loss solver that significantly improves its robustness on MNIST and all other datasets and retains clean test accuracy. Finally we show practical applications of our method to deter traffic sign and facial recognition adversarial attacks. We discuss attacks with 01 loss, substitute model accuracy, and several future avenues like multiclass, 01 loss convolutions, and further adversarial training.

How far apart are two neural networks? This is a foundational question in their theory. We derive a simple and tractable bound that relates distance in function space to distance in parameter space for a broad class of nonlinear compositional functions. The bound distills a clear dependence on depth of the composition. The theory is of practical relevance since it establishes a trust region for first-order optimisation. In turn, this suggests an optimiser that we call Frobenius matched gradient descent---or Fromage. Fromage involves a principled form of gradient rescaling and enjoys guarantees on stability of both the spectra and Frobenius norms of the weights. We find that the new algorithm increases the depth at which a multilayer perceptron may be trained as compared to Adam and SGD and is competitive with Adam for training generative adversarial networks. We further verify that Fromage scales up to a language transformer with over $10^8$ parameters. Please find code & reproducibility instructions at: https://github.com/jxbz/fromage.

Graph distance metric learning serves as the foundation for many graph learning problems, e.g., graph clustering, graph classification and graph matching. Existing research works on graph distance metric (or graph kernels) learning fail to maintain the basic properties of such metrics, e.g., non-negative, identity of indiscernibles, symmetry and triangle inequality, respectively. In this paper, we will introduce a new graph neural network based distance metric learning approaches, namely GB-DISTANCE (GRAPH-BERT based Neural Distance). Solely based on the attention mechanism, GB-DISTANCE can learn graph instance representations effectively based on a pre-trained GRAPH-BERT model. Different from the existing supervised/unsupervised metrics, GB-DISTANCE can be learned effectively in a semi-supervised manner. In addition, GB-DISTANCE can also maintain the distance metric basic properties mentioned above. Extensive experiments have been done on several benchmark graph datasets, and the results demonstrate that GB-DISTANCE can out-perform the existing baseline methods, especially the recent graph neural network model based graph metrics, with a significant gap in computing the graph distance.

Supervised machine learning algorithms have seen spectacular advances and surpassed human level performance in a wide range of specific applications. However, using complex ensemble or deep learning algorithms typically results in black box models, where the path leading to individual predictions cannot be followed in detail. In order to address this issue, we propose the novel "Cyclic Boosting" machine learning algorithm, which allows to efficiently perform accurate regression and classification tasks while at the same time allowing a detailed understanding of how each individual prediction was made.