We provide initial seedings to the Quick Shift clustering algorithm, which approximate the locally high-density regions of the data. Such seedings act as more stable and expressive cluster-cores than the singleton modes found by Quick Shift. We establish statistical consistency guarantees for this modification. We then show strong clustering performance on real datasets as well as promising applications to image segmentation.

Many recent works on knowledge distillation have provided ways to transfer the knowledge of a trained network for improving the learning process of a new one, but finding a good technique for knowledge distillation is still an open problem. In this paper, we provide a new perspective based on a decision boundary, which is one of the most important component of a classifier. The generalization performance of a classifier is closely related to the adequacy of its decision boundary, so a good classifier bears a good decision boundary. Therefore, transferring information closely related to the decision boundary can be a good attempt for knowledge distillation. To realize this goal, we utilize an adversarial attack to discover samples supporting a decision boundary. Based on this idea, to transfer more accurate information about the decision boundary, the proposed algorithm trains a student classifier based on the adversarial samples supporting the decision boundary. Experiments show that the proposed method indeed improves knowledge distillation and achieves the state-of-the-arts performance.

Hi all, I'm doing research with some signals and I'd like to make some predictions based on some signals I have. These are of unequal length. There are three sensors that measure the same activity. There are two labels per sequence. Each sequence corresponds to two values, say 2 and 1.

For me, studying Logistic regression first helped a lot when I started to learn Neural Networks. You can think of each neuron in the network as a Logistic Regression, it has the input, the weights, the bias you do a dot product to all of that, then apply some non linear function. Moreover, the final layer of a neural network is a simple linear model (most of the time). Let's look closer at the "output layer", you can see that this is a simple linear (or logistic) regression, we have the input (hidden layer 2), we have the weighs, we do a dot product and then add a non linear function (depends on the task). The first part (on the left) is trying to learn a good representation of the data that will help the second part (on the right) to perform a linear classification/regression.

This is the second Udemy class on Matlab I've taken. Already, a couple important concepts have been discussed that weren't discussed in the previous course. I'm glad the instructor is comparing Matlab to Excel, which is the tool I've been using and have been frustrated with. This course is a little more advanced than the previous course I took. As an engineer, I'm delighted it covers complex numbers, derivatives, and integrals.

It is important to distinguish prediction and classification. In many decisionmaking contexts, classification represents a premature decision, because classification combines prediction and decision making and usurps the decision maker in specifying costs of wrong decisions. The classification rule must be reformulated if costs/utilities or sampling criteria change. Predictions are separate from decisions and can be used by any decision maker. Classification is best used with non-stochastic/deterministic outcomes that occur frequently, and not when two individuals with identical inputs can easily have different outcomes.

We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a piecewise constant image representation with sparse region boundaries and sparse cluster value scattering. The resultant piecewise flat embedding exhibits interesting properties such as suppressing slowly varying signals, and offers an image representation with higher region identifiability which is desirable for image segmentation or high-level semantic analysis tasks. We formulate our embedding as a variant of the Laplacian Eigenmap embedding with an $L_{1,p} (0

Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper, we study a family of objective functions formed by truncating traditional loss functions, which is applicable to both shallow learning and deep learning. Truncating loss functions has potential to be less vulnerable and more robust to large noise in observations that could be adversarial. More importantly, it is a generic technique without assuming the knowledge of noise distribution. To justify non-convex learning with truncated losses, we establish excess risk bounds of empirical risk minimization based on truncated losses for heavy-tailed output, and statistical error of an approximate stationary point found by stochastic gradient descent (SGD) method. Our experiments for shallow and deep learning for regression with outliers, corrupted data and heavy-tailed noise further justify the proposed method.

This paper presents a novel approach to kernel tuning. The method presented borrows techniques from reproducing kernel Banach space (RKBS) theory and tensor kernels and leverages them to convert (re-weight in feature space) existing kernel functions into new, problem-specific kernels using auxiliary data. The proposed method is applied to accelerating Bayesian optimisation via covariance (kernel) function pre-tuning for short-polymer fibre manufacture and alloy design.

Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to $\log(\frac{1}{\epsilon})$ for the smooth and strongly convex objective. This complexity result is especially significant in learning problem, as the overwhelming data size makes a single evluation of gradient computational expensive. However, in high-dimensional statistical estimation problems, the objective is typically not strongly convex, and sometimes even non-convex. In this paper, we extend the state-of-the-art FW type algorithms for the large-scale, high-dimensional estimation problem. We show that as long as the objective satisfies {\em restricted strong convexity}, and we are not optimizing over statistical limit of the model, the $\log(\frac{1}{\epsilon})$ gradient evaluation complexity could still be attained.