In this paper, we apply machine learning to distributed private data owned by multiple data owners, entities with access to non-overlapping training datasets. We use noisy, differentially-private gradients to minimize the fitness cost of the machine learning model using stochastic gradient descent. We quantify the quality of the trained model, using the fitness cost, as a function of privacy budget and size of the distributed datasets to capture the trade-off between privacy and utility in machine learning. This way, we can predict the outcome of collaboration among privacy-aware data owners prior to executing potentially computationally-expensive machine learning algorithms. Particularly, we show that the difference between the fitness of the trained machine learning model using differentially-private gradient queries and the fitness of the trained machine model in the absence of any privacy concerns is inversely proportional to the size of the training datasets squared and the privacy budget squared. We successfully validate the performance prediction with the actual performance of the proposed privacy-aware learning algorithms, applied to: financial datasets for determining interest rates of loans using regression; and detecting credit card frauds using support vector machines.

Pathologists find tedious to examine the status of the sentinel lymph node on a large number of pathological scans. The examination process of such lymph node which encompasses metastasized cancer cells is histopathologically organized. However, the task of finding metastatic tissues is gradual which is often challenging. In this work, we present our deep convolutional neural network based model validated on PatchCamelyon (PCam) benchmark dataset for fundamental machine learning research in histopathology diagnosis. We find that our proposed model trained with a semi-supervised learning approach by using pseudo labels on PCam-level significantly leads to better performances to strong CNN baseline on the AUC metric.

Mixed Integer Programming (MIP) is one of the most widely used modeling techniques to deal with combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model structures and solution appearances but differing in formulation coefficients. This offers the opportunity for machine learning method to explore the correlations between model structures and the resulting solution values. To address this issue, we propose to represent an MIP instance using a tripartite graph, based on which a Graph Convolutional Network (GCN) is constructed to predict solution values for binary variables. The predicted solutions are used to generate a local branching cut to the model which accelerate the solution process for MIP. Computational evaluations on 8 distinct types of MIP problems show that the proposed framework improves the performance of a state-of-the-art open source MIP solver significantly in terms of running time and solution quality.

Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully applied to learn maps across high-dimensional domains. However, little is known about the nature of the map learned with a GAN objective. To address this problem, we propose a generative adversarial model in which the discriminator's objective is the $2$-Wasserstein metric. We show that during training, our generator follows the $W_2$-geodesic between the initial and the target distributions. As a consequence, it reproduces an optimal map at the end of training. We validate our approach empirically in both low-dimensional and high-dimensional continuous settings, and show that it outperforms prior methods on image data.

Many articles and books considered the assessment of classifiers using simulated and real-world datasets (e.g., (Raudys and Pikelis, 1980; Efron and Tibshirani, 1997; Hastie et al., 2001)); but none of them considered a systematic assessment of NCC. However, Inselberg and Avidan (2000) compared NCC with other classifiers only on few real high-dimensional datasets; that study mentioned the superiority of NCC over other classifiers. NCC, as described below, builds decision regions geometrically using convex hulls. This partitioning mechanism has a drawback on the performance of the NCC (as explained in Section 3). NCC classifies any testing observation--regardless to its class, whether "class 1" or "class 2"--as class, say, "class 2" as long as it does not lie inside the range of the training data set; i.e., within the minimum and maximum values of each dimension. Since this is not always true, the present article proposes combining NCC with LDA to classify observations outside the range of the training set.

We study the problem of detecting critical structures using a graph embedding model. Existing graph embedding models lack the ability to precisely detect critical structures that are specific to a task at the global scale. In this paper, we propose a novel graph embedding model, called the Ego-CNNs, that employs the ego-convolutions convolutions at each layer and stacks up layers using an ego-centric way to detects precise critical structures efficiently. An Ego-CNN can be jointly trained with a task model and help explain/discover knowledge for the task. We conduct extensive experiments and the results show that Ego-CNNs (1) can lead to comparable task performance as the state-of-the-art graph embedding models, (2) works nicely with CNN visualization techniques to illustrate the detected structures, and (3) is efficient and can incorporate with scale-free priors, which commonly occurs in social network datasets, to further improve the training efficiency.

The emergence of one-shot approaches has greatly advanced the research on neural architecture search (NAS). Recent approaches train an over-parameterized super-network (one-shot model) and then sample and evaluate a number of sub-networks, which inherit weights from the one-shot model. The overall searching cost is significantly reduced as training is avoided for sub-networks. However, the network sampling process is casually treated and the inherited weights from an independently trained super-network perform sub-optimally for sub-networks. In this paper, we propose a novel one-shot NAS scheme to address the above issues. The key innovation is to explicitly estimate the joint a posteriori distribution over network architecture and weights, and sample networks for evaluation according to it. This brings two benefits. First, network sampling under the guidance of a posteriori probability is more efficient than conventional random or uniform sampling. Second, the network architecture and its weights are sampled as a pair to alleviate the sub-optimal weights problem. Note that estimating the joint a posteriori distribution is not a trivial problem. By adopting variational methods and introducing a hybrid network representation, we convert the distribution approximation problem into an end-to-end neural network training problem which is neatly approached by variational dropout. As a result, the proposed method reduces the number of sampled sub-networks by orders of magnitude. We validate our method on the fundamental image classification task. Results on Cifar-10, Cifar-100 and ImageNet show that our method strikes the best trade-off between precision and speed among NAS methods. On Cifar-10, we speed up the searching process by 20x and achieve a higher precision than the best network found by existing NAS methods.

Sample inefficiency is a long-lasting problem in reinforcement learning (RL). The state-of-the-art uses value function to derive policy while it usually requires an extensive search over the state-action space, which is one reason for the inefficiency. Towards the sample-efficient RL, we propose ranking policy gradient (RPG), a policy gradient method that learns the optimal ranking of a set of discrete actions. To accelerate the learning of policy gradient methods, we describe a novel off-policy learning framework and establish the equivalence between maximizing the lower bound of return and imitating a near-optimal policy without accessing any oracles. These results lead to a general sample-efficient off-policy learning framework, which accelerates learning and reduces variance. Furthermore, the sample complexity of RPG does not depend on the dimension of state space, which enables RPG for large-scale problems. We conduct extensive experiments showing that when consolidating with the off-policy learning framework, RPG substantially reduces the sample complexity, comparing to the state-of-the-art.

In machine learning, the effectiveness of a network is measured by an error function which measures how good a network is at its job. In general, the higher the error, the worse the network is. Conversely, the lower the error, the better the network is. When a machine is trying to learn how to do a task, it tries to make as few mistakes as possible; that is, minimize its error function. True gradient descent is the application of gradient descent to a machine learning network to minimize an error function.

A myriad of options exist for classification. That said, three popular classification methods-- Decision Trees, k-NN & Naive Bayes--can be tweaked for practically every situation. Naive Bayes and K-NN, are both examples of supervised learning (where the data comes already labeled). Decision trees are easy to use for small amounts of classes. If you're trying to decide between the three, your best option is to take all three for a test drive on your data, and see which produces the best results.