In this paper, a novel K-Nearest Neighbour and Support Vector Machine hybrid classification technique has been proposed that is simple and robust. It is based on the concept of discriminative nearest neighbourhood classification. The technique consists of using K-Nearest Neighbour Classification for test samples satisfying a proximity condition. The patterns which do not pass the proximity condition are separated. This is followed by sifting the training set for a fixed number of patterns for every class which are closest to each separated test pattern respectively, based on the Euclidean distance metric. Subsequently, for every separated test sample, a Support Vector Machine is trained on the sifted training set patterns associated with it, and classification for the test sample is done. The proposed technique has been compared to the state of art in this research area. Three datasets viz. the United States Postal Service (USPS) Handwritten Digit Dataset, MNIST Dataset, and an Arabic numeral dataset, the Modified Arabic Digits Database, MADB, have been used to evaluate the performance of the algorithm. The algorithm generally outperforms the other algorithms with which it has been compared.

The probabilistic classification vector machine (PCVM) synthesizes the advantages of both the support vector machine and the relevant vector machine, delivering a sparse Bayesian solution to classification problems. However, the PCVM is currently only applicable to binary cases. Extending the PCVM to multi-class cases via heuristic voting strategies such as one-vs-rest or one-vs-one often results in a dilemma where classifiers make contradictory predictions, and those strategies might lose the benefits of probabilistic outputs. To overcome this problem, we extend the PCVM and propose a multi-class probabilistic classification vector machine (mPCVM). Two learning algorithms, i.e., one top-down algorithm and one bottom-up algorithm, have been implemented in the mPCVM. The top-down algorithm obtains the maximum a posteriori (MAP) point estimates of the parameters based on an expectation-maximization algorithm, and the bottom-up algorithm is an incremental paradigm by maximizing the marginal likelihood. The superior performance of the mPCVMs, especially when the investigated problem has a large number of classes, is extensively evaluated on synthetic and benchmark data sets.

Despite the popularism of Bayesian neural networks in recent years, its use is somewhat limited in complex and big data situations due to the computational cost associated with full posterior evaluations. Variational Bayes (VB) provides a useful alternative to circumvent the computational cost and time complexity associated with the generation of samples from the true posterior using Markov Chain Monte Carlo (MCMC) techniques. The efficacy of the VB methods is well established in machine learning literature. However, its potential broader impact is hindered due to a lack of theoretical validity from a statistical perspective. However there are few results which revolve around the theoretical properties of VB, especially in non-parametric problems. In this paper, we establish the fundamental result of posterior consistency for the mean-field variational posterior (VP) for a feed-forward artificial neural network model. The paper underlines the conditions needed to guarantee that the VP concentrates around Hellinger neighborhoods of the true density function. Additionally, the role of the scale parameter and its influence on the convergence rates has also been discussed. The paper mainly relies on two results (1) the rate at which the true posterior grows (2) the rate at which the KL-distance between the posterior and variational posterior grows. The theory provides a guideline of building prior distributions for Bayesian NN models along with an assessment of accuracy of the corresponding VB implementation.

Bayesian optimization is a sequential decision making framework for optimizing expensive-to-evaluate black-box functions. Computing a full lookahead policy amounts to solving a highly intractable stochastic dynamic program. Myopic approaches, such as expected improvement, are often adopted in practice, but they ignore the long-term impact of the immediate decision. Existing nonmyopic approaches are mostly heuristic and/or computationally expensive. In this paper, we provide the first efficient implementation of general multi-step lookahead Bayesian optimization, formulated as a sequence of nested optimization problems within a multi-step scenario tree. Instead of solving these problems in a nested way, we equivalently optimize all decision variables in the full tree jointly, in a ``one-shot'' fashion. Combining this with an efficient method for implementing multi-step Gaussian process ``fantasization,'' we demonstrate that multi-step expected improvement is computationally tractable and exhibits performance superior to existing methods on a wide range of benchmarks.

In real-world machine learning applications, even well-curated training datasets have various types of heterogeneity. Two main types of heterogeneity are: (1) data imbalance: the input or label distribution often has a long-tailed density, and (2) heteroskedasticity: the labels given inputs have varying levels of uncertainties across subsets of data stemming from various sources such as the intrinsic ambiguity of the data or annotation errors. Many deep learning algorithms have been proposed for imbalanced datasets (e.g., see [Wang et al., 2017, Cao et al., 2019, Cui et al., 2019, Liu et al., 2019] and the reference therein). However, heteroskedasticity, a classical notion studied extensively in the statistical community [Pintore et al., 2006, Wang et al., 2013, Tibshirani et al., 2014], has so far been under-explored in deep learning. This paper focuses on addressing heteroskedasticity and its interaction with data imbalance in deep learning. Heteroskedasticity is often studied in regression analysis and refers to the property that the distribution of the error varies across inputs. In this work, we mostly focus on classification, though the developed technique also applies to regression. Here, heteroskedasticity reflects how the uncertainty in the conditional distribution p(y x), or the entropy of y x, varies as a function of x .

Graph neural networks are promising architecture for learning and inference with graph-structured data. Yet difficulties in modelling the ``parts'' and their ``interactions'' still persist in terms of graph classification, where graph-level representations are usually obtained by squeezing the whole graph into a single vector through graph pooling. From complex systems point of view, mixing all the parts of a system together can affect both model interpretability and predictive performance, because properties of a complex system arise largely from the interaction among its components. We analyze the intrinsic difficulty in graph classification under the unified concept of ``resolution dilemmas'' with learning theoretic recovery guarantees, and propose ``SLIM'', an inductive neural network model for Structural Landmarking and Interaction Modelling. It turns out, that by solving the resolution dilemmas, and leveraging explicit interacting relation between component parts of a graph to explain its complexity, SLIM is more interpretable, accurate, and offers new insight in graph representation learning.

Multiple sequences alignment (MSA) is a traditional and challenging task for time-series analyses. The MSA problem is formulated as a discrete optimization problem and is typically solved by dynamic programming. However, the computational complexity increases exponentially with respect to the number of input sequences. In this paper, we propose neural time warping (NTW) that relaxes the original MSA to a continuous optimization and obtains the alignments using a neural network. The solution obtained by NTW is guaranteed to be a feasible solution for the original discrete optimization problem under mild conditions. Our experimental results show that NTW successfully aligns a hundred time-series and significantly outperforms existing methods for solving the MSA problem. In addition, we show a method for obtaining average time-series data as one of applications of NTW. Compared to the existing barycenters, the mean time series data retains the features of the input time-series data.

Neural networks have achieved state of the art results across several domains such as computer vision, language processing, and reinforcement learning. This performance is generally contingent on large, over-parameterized networks that are trained using massive amounts of data. For example, the current state of the art on the ImageNet classification task uses a network with over 480 million parameters [TVDJ20], and consequently, the best performing networks are prohibitive in terms of computational and memory requirements. Therefore, compressing neural networks is vital for resource limited settings (such as self-driving cars and mobile devices). In this work, we present an algorithm for compressing neural networks to far higher degree of sparsity levels than has been reported in the literature.

The causal explanation of image misclassifications is an understudied niche, which can potentially provide valuable insights in model interpretability and increase prediction accuracy. This study trains CIFAR-10 on six modern CNN architectures, including VGG16, ResNet50, GoogLeNet, DenseNet161, MobileNet V2, and Inception V3, and explores the misclassification patterns using conditional confusion matrices and misclassification networks. Two causes are identified and qualitatively distinguished: morphological similarity and non-essential information interference. The former cause is not model dependent, whereas the latter is inconsistent across all six models. To reduce the misclassifications caused by non-essential information interference, this study erases the pixels within the bonding boxes anchored at the top 5% pixels of the saliency map. This method first verifies the cause; then by directly modifying the cause it reduces the misclassification. Future studies will focus on quantitatively differentiating the two causes of misclassifications, generalizing the anchor-box based inference modification method to reduce misclassification, exploring the interactions of the two causes in misclassifications.

Human action recognition is one of the important fields of computer vision and machine learning. Although various methods have been proposed for 3D action recognition, some of which are basic and some use deep learning, the need of basic methods based on generalized eigenvalue problem is sensed for action recognition. This need is especially sensed because of having similar basic methods in the field of face recognition such as eigenfaces and Fisherfaces. In this paper, we propose Roweisposes which uses Roweis discriminant analysis for generalized subspace learning. This method includes Fisherposes, eigenposes, supervised eigenposes, and double supervised eigenposes as its special cases. Roweisposes is a family of infinite number of action recongition methods which learn a discriminative subspace for embedding the body poses. Experiments on the TST, UTKinect, and UCFKinect datasets verify the effectiveness of the proposed method for action recognition.