Classification is the most important process in data analysis. However, due to the inherent non-convex and non-smooth structure of the zero-one loss function of the classification model, various convex surrogate loss functions such as hinge loss, squared hinge loss, logistic loss, and exponential loss are introduced. These loss functions have been used for decades in diverse classification models, such as SVM (support vector machine) with hinge loss, logistic regression with logistic loss, and Adaboost with exponential loss and so on. In this work, we present a Perceptron-augmented convex classification framework, {\it Logitron}. The loss function of it is a smoothly stitched function of the extended logistic loss with the famous Perceptron loss function. The extended logistic loss function is a parameterized function established based on the extended logarithmic function and the extended exponential function. The main advantage of the proposed Logitron classification model is that it shows the connection between SVM and logistic regression via polynomial parameterization of the loss function. In more details, depending on the choice of parameters, we have the Hinge-Logitron which has the generalized $k$-th order hinge-loss with an additional $k$-th root stabilization function and the Logistic-Logitron which has a logistic-like loss function with relatively large $|k|$. Interestingly, even $k=-1$, Hinge-Logitron satisfies the classification-calibration condition and shows reasonable classification performance with low computational cost. The numerical experiment in the linear classifier framework demonstrates that Hinge-Logitron with $k=4$ (the fourth-order SVM with the fourth root stabilization function) outperforms logistic regression, SVM, and other Logitron models in terms of classification accuracy.

Our problem of interest is to cluster vertices of a graph by identifying its underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods, because it is easy to implement while often outperforming traditional clustering algorithms. However, there are two inherent model selection problems in spectral clustering, namely estimating the embedding dimension and number of clusters. This paper attempts to address the issue by establishing a novel model selection framework specifically for vertex clustering on graphs under a stochastic block model. The first contribution is a probabilistic model which approximates the distribution of the extended spectral embedding of a graph. The model is constructed based on a theoretical result of asymptotic normality of the informative part of the embedding, and on a simulation result of limiting behavior of the redundant part of the embedding. The second contribution is a simultaneous model selection framework. In contrast with the traditional approaches, our model selection procedure estimates embedding dimension and number of clusters simultaneously. Based on our proposed distributional model, a theorem on the consistency of the estimates of model parameters is stated and proven. The theorem provides a statistical support for the validity of our method. Heuristic algorithms via the simultaneous model selection framework for vertex clustering are proposed, with good performance shown in the experiment on synthetic data and on the real application of connectome analysis.

Objective: A variety of pattern analysis techniques for model training in brain interfaces exploit neural feature dimensionality reduction based on feature ranking and selection heuristics. In the light of broad evidence demonstrating the potential sub-optimality of ranking based feature selection by any criterion, we propose to extend this focus with an information theoretic learning driven feature transformation concept. Methods: We present a maximum mutual information linear transformation (MMI-LinT), and a nonlinear transformation (MMI-NonLinT) framework derived by a general definition of the feature transformation learning problem. Empirical assessments are performed based on electroencephalographic (EEG) data recorded during a four class motor imagery brain-computer interface (BCI) task. Exploiting state-of-the-art methods for initial feature vector construction, we compare the proposed approaches with conventional feature selection based dimensionality reduction techniques which are widely used in brain interfaces. Furthermore, for the multi-class problem, we present and exploit a hierarchical graphical model based BCI decoding system. Results: Both binary and multi-class decoding analyses demonstrate significantly better performances with the proposed methods. Conclusion: Information theoretic feature transformations are capable of tackling potential confounders of conventional approaches in various settings. Significance: We argue that this concept provides significant insights to extend the focus on feature selection heuristics to a broader definition of feature transformation learning in brain interfaces.

Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which adapt themselves to obtain better estimators over iterations. Although it is straightforward to show that they have the same $\mathcal{O}(1/\sqrt{N})$ convergence rate as the importance sampling where $N$ is the number of Monte Carlo samples, the behaviour of adaptive importance samplers over the number of iterations has been left relatively unexplored despite these adaptive algorithms aim at improving the proposal quality iteratively. In this work, we explore an adaptation strategy based on convex optimisation which leads to a class of adaptive importance samplers, termed optimised adaptive importance samplers (OAIS). These samplers rely on an adaptation idea based on minimizing the $\chi^2$-divergence between an exponential family proposal and the target. The analysed algorithms are closely related to the adaptive importance samplers which minimise the variance of the weight function. We first prove non-asymptotic error bounds for the mean squared errors (MSEs) of these algorithms, which explicitly depend on the number of iterations and the number of particles together. The non-asymptotic bounds derived in this paper imply that when the target is from the exponential family, the $L_2$ errors of the optimised samplers converge to the perfect Monte Carlo sampling error $\mathcal{O}(1/\sqrt{N})$. We also show that when the target is not from the exponential family, the asymptotic error rate is $\mathcal{O}(\sqrt{\rho^\star/N})$ where $\rho^\star$ is the minimum $\chi^2$-divergence between the target and an exponential family proposal.

In order to enable high-quality decision making and motion planning of intelligent systems such as robotics and autonomous vehicles, accurate probabilistic predictions for surrounding interactive objects is a crucial prerequisite. Although many research studies have been devoted to making predictions on a single entity, it remains an open challenge to forecast future behaviors for multiple interactive agents simultaneously. In this work, we take advantage of the Generative Adversarial Network (GAN) due to its capability of distribution learning and propose a generic multi-agent probabilistic prediction and tracking framework which takes the interactions among multiple entities into account, in which all the entities are treated as a whole. However, since GAN is very hard to train, we make an empirical research and present the relationship between training performance and hyperparameter values with a numerical case study. The results imply that the proposed model can capture both the mean, variance and multi-modalities of the groundtruth distribution. Moreover, we apply the proposed approach to a real-world task of vehicle behavior prediction to demonstrate its effectiveness and accuracy. The results illustrate that the proposed model trained by adversarial learning can achieve a better prediction performance than other state-of-the-art models trained by traditional supervised learning which maximizes the data likelihood. The well-trained model can also be utilized as an implicit proposal distribution for particle filtered based Bayesian state estimation.

Ubiquitous cyber-intrusions endanger the security of our devices constantly. They may bring irreversible damages to the system and cause leakage of privacy. Thus, it is of vital importance to promptly detect these intrusions. Traditional methods such as Decision Trees and Support Vector Machine (SVM) are used to classify normal internet connections and cyber-intrusions. However, the intrusions are largely fewer than normal connections, which limits the capability of these methods. Anomaly detection methods such as Isolation Forest can handle the imbalanced data. Nevertheless, when the features of data increase, these methods lack enough ability to learn the distribution. Generative adversarial network (GAN) has been proposed to solve the above issues. With its strong generative ability, it only needs to learn the distribution of normal status, and identify the abnormal status when intrusion occurs. But existing models are not suitable to process discrete values, leading to immense degradation of detection performance. To cope with these challenges, in this paper, we propose a novel GAN-based model with specifically-designed loss function to detect cyber-intrusions. Experiment results show that our model outperforms state-of-the-art models and remarkably reduce the overhead.

Dictionary learning is a dimensionality reduction technique widely used in data mining, machine learning and signal processing alike. Nevertheless, many dictionary learning algorithms such as variants of Matrix Factorization (MF) do not adequately scale with the size of available datasets. Furthermore, scalable dictionary learning methods lack interpretability of the derived dictionary matrix. To mitigate these two issues, we propose a novel low-complexity, batch online convex dictionary learning algorithm. The algorithm sequentially processes small batches of data maintained in a fixed amount of storage space, and produces meaningful dictionaries that satisfy convexity constraints. Our analytical results are two-fold. First, we establish convergence guarantees for the proposed online learning scheme. Second, we show that a subsequence of the generated dictionaries converges to a stationary point of the approximation-error function. Experimental results on synthetic and real world datasets demonstrate both the computational savings of the proposed online method with respect to convex non-negative MF, and performance guarantees comparable to those of online non-convex learning.

The field of image reconstruction has undergone four waves of methods. The first wave was analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. The second wave was iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. The third wave of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. The fourth wave of methods replaces mathematically designed models of signals and processes with data-driven or adaptive models inspired by the field of machine learning. This paper reviews the progress in image reconstruction methods with focus on the two most recent trends: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

How can we measure whether a natural language generation system produces both high quality and diverse outputs? Human evaluation captures quality but not diversity, as it does not catch models that simply plagiarize from the training set. On the other hand, statistical evaluation (i.e., perplexity) captures diversity but not quality, as models that occasionally emit low quality samples would be insufficiently penalized. In this paper, we propose a unified framework which evaluates both diversity and quality, based on the optimal error rate of predicting whether a sentence is human- or machine-generated. We demonstrate that this error rate can be efficiently estimated by combining human and statistical evaluation, using an evaluation metric which we call HUSE. On summarization and chit-chat dialogue, we show that (i) HUSE detects diversity defects which fool pure human evaluation and that (ii) techniques such as annealing for improving quality actually decrease HUSE due to decreased diversity.

While Standard gradient descent is one very popular optimisation method, its convergence cannot be proven beyond the class of functions whose gradient is globally Lipschitz continuous. As such, it is not actually applicable to realistic applications such as Deep Neural Networks. In this paper, we prove that its backtracking variant behaves very nicely, in particular convergence can be shown for all Morse functions. The main theoretical result of this paper is as follows. Theorem. Let $f:\mathbb{R}^k\rightarrow \mathbb{R}$ be a $C^1$ function, and $\{z_n\}$ a sequence constructed from the Backtracking gradient descent algorithm. (1) Either $\lim _{n\rightarrow\infty}||z_n||=\infty$ or $\lim _{n\rightarrow\infty}||z_{n+1}-z_n||=0$. (2) Assume that $f$ has at most countably many critical points. Then either $\lim _{n\rightarrow\infty}||z_n||=\infty$ or $\{z_n\}$ converges to a critical point of $f$. (3) More generally, assume that all connected components of the set of critical points of $f$ are compact. Then either $\lim _{n\rightarrow\infty}||z_n||=\infty$ or $\{z_n\}$ is bounded. Moreover, in the latter case the set of cluster points of $\{z_n\}$ is connected. Some generalised versions of this result, including an inexact version, are included. Another result in this paper concerns the problem of saddle points. We then present a heuristic argument to explain why Standard gradient descent method works so well, and modifications of the backtracking versions of GD, MMT and NAG. Experiments with datasets CIFAR10 and CIFAR100 on various popular architectures verify the heuristic argument also for the mini-batch practice and show that our new algorithms, while automatically fine tuning learning rates, perform better than current state-of-the-art methods such as MMT, NAG, Adagrad, Adadelta, RMSProp, Adam and Adamax.