As network data become increasingly available, new opportunities arise to understand dynamic and multilayer network systems in many applied disciplines. Statistical modeling for multilayer networks is currently an active research area that aims to develop methods to carry out inference on such data. Recent contributions focus on latent space representation of the multilayer structure with underlying stochastic processes to account for network dynamics. Existing multilayer models are however typically limited to rather small networks. In this paper we introduce a dynamic multilayer block network model with a latent space represention for blocks rather than nodes. A block structure is natural for many real networks, such as social or transportation networks, where community structure naturally arises. A Gibbs sampler based on P\'olya-Gamma data augmentation is presented for the proposed model. Results from extensive simulations on synthetic data show that the inference algorithm scales well with the size of the network. We present a case study using real data from an airline system, a classic example of hub-and-spoke network.

These figures compare validation error for hyperparameter optimization of an image classification neural network with random search in grey and Bayesian Optimization (using the Tree Parzen Estimator or TPE) in green. Lower is better: a smaller validation set error generally means better test set performance, and a smaller number of trials means less time invested. Clearly, there are significant advantages to Bayesian methods, and these graphs, along with other impressive results, convinced me it was time to take the next step and learn model-based hyperparameter optimization. The one-sentence summary of Bayesian hyperparameter optimization is: build a probability model of the objective function and use it to select the most promising hyperparameters to evaluate in the true objective function. If you like to operate at a very high level, then this sentence may be all you need. However, if you want to understand the details, this article is my attempt to outline the concepts behind Bayesian optimization, in particular Sequential Model-Based Optimization (SMBO) with the Tree Parzen Estimator (TPE).

We are going to use the Heart Disease Data Set provided by Machine Learning Repository of University of California. The UCI page mentions following as the principal investigator responsible for the data collection: 1. Hungarian Institute of Cardiology. In this project we are going to classify whether the chest pain is the indication of Heart Disease or not by using the person's Age, Sex, Type of Chest Pain, Blood Pressure, Cholesterol Level and their Heart Disease status data. First of all let's look at our Data Dictionary: Here we have total of 14 columns, 13 columns for our features and 1 column for the label. We are using pandas for data processing.

We are going to use the Heart Disease Data Set provided by Machine Learning Repository of University of California. The UCI page mentions following as the principal investigator responsible for the data collection: 1. Hungarian Institute of Cardiology. In this project we are going to classify whether the chest pain is the indication of Heart Disease or not by using the person's Age, Sex, Type of Chest Pain, Blood Pressure, Cholesterol Level and their Heart Disease status data. First of all let's look at our Data Dictionary: Here we have total of 14 columns, 13 columns for our features and 1 column for the label. We are using pandas for data processing.

In this paper, we investigate learning temporal abstractions in cooperative multi-agent systems using the options framework (Sutton et al, 1999) and provide a model-free algorithm for this problem. First, we address the planning problem for the decentralized POMDP represented by the multi-agent system, by introducing a common information approach. We use common beliefs and broadcasting to solve an equivalent centralized POMDP problem. Then, we propose the Distributed Option Critic (DOC) algorithm, motivated by the work of Bacon et al (2017) in the single-agent setting. Our approach uses centralized option evaluation and decentralized intra-option improvement. We analyze theoretically the asymptotic convergence of DOC and validate its performance in grid-world environments, where we implement DOC using a deep neural network. Our experiments show that DOC performs competitively with state-of-the-art algorithms and that it is scalable when the number of agents increases.

Regions of high-dimensional input spaces that are un-derrepresented in training datasets reduce machine-learnt classifier performance, and may lead to corner cases and unwanted bias for classifiers used in decision making systems. When these regions belong to otherwise well-represented classes, their presence and negative impact are very hard to identify. We propose an approach for the detection and mitigation of such rare subclasses in neural network classifiers. The new approach is underpinned by an easy-to-compute commonality metric that supports the detection of rare subclasses, and comprises methods for reducing their impact during both model training and model exploitation.

Dropout has been proven to be an effective algorithm for training robust deep networks because of its ability to prevent overfitting by avoiding the co-adaptation of feature detectors. Current explanations of dropout include bagging, naive Bayes, regularization, and sex in evolution. According to the activation patterns of neurons in the human brain, when faced with different situations, the firing rates of neurons are random and continuous, not binary as current dropout does. Inspired by this phenomenon, we extend the traditional binary dropout to continuous dropout. On the one hand, continuous dropout is considerably closer to the activation characteristics of neurons in the human brain than traditional binary dropout. On the other hand, we demonstrate that continuous dropout has the property of avoiding the co-adaptation of feature detectors, which suggests that we can extract more independent feature detectors for model averaging in the test stage. We introduce the proposed continuous dropout to a feedforward neural network and comprehensively compare it with binary dropout, adaptive dropout, and DropConnect on MNIST, CIFAR-10, SVHN, NORB, and ILSVRC-12. Thorough experiments demonstrate that our method performs better in preventing the co-adaptation of feature detectors and improves test performance. The code is available at: https://github.com/jasonustc/caffe-multigpu/tree/dropout.

Paired estimation of change in parameters of interest over a population plays a central role in several application domains including those in the social sciences, epidemiology, medicine and biology. In these domains, the size of the population under study is often very large, however, the number of observations available per individual in the population is very small (\emph{sparse observations}) which makes the problem challenging. Consider the setting with $N$ independent individuals, each with unknown parameters $(p_i, q_i)$ drawn from some unknown distribution on $[0, 1]^2$. We observe $X_i \sim \text{Bin}(t, p_i)$ before an event and $Y_i \sim \text{Bin}(t, q_i)$ after the event. Provided these paired observations, $\{(X_i, Y_i) \}_{i=1}^N$, our goal is to accurately estimate the \emph{distribution of the change in parameters}, $\delta_i := q_i - p_i$, over the population and properties of interest like the \emph{$\ell_1$-magnitude of the change} with sparse observations ($t\ll N$). We provide \emph{information theoretic lower bounds} on the error in estimating the distribution of change and the $\ell_1$-magnitude of change. Furthermore, we show that the following two step procedure achieves the optimal error bounds: first, estimate the full joint distribution of the paired parameters using the maximum likelihood estimator (MLE) and then estimate the distribution of change and the $\ell_1$-magnitude of change using the joint MLE. Notably, and perhaps surprisingly, these error bounds are of the same order as the minimax optimal error bounds for learning the \emph{full} joint distribution itself (in Wasserstein-1 distance); in other words, estimating the magnitude of the change of parameters over the population is, in a minimax sense, as difficult as estimating the full joint distribution itself.

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits from a causal perspective. The identified variables and models allow for a concise description of the dynamics across multiple experimental settings and can be used for prediction in unseen experiments. We observe significant improvements compared to well established approaches focusing solely on predictive performance, especially for out-of-sample generalization.

After every weekend session you'll need to solve assignments until next week.