Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, with a training objective that makes them approximately sample in proportion to a given reward function. In this paper, we show a number of additional theoretical properties of GFlowNets. They can be used to estimate joint probability distributions and the corresponding marginal distributions where some variables are unspecified and, of particular interest, can represent distributions over composite objects like sets and graphs. GFlowNets amortize the work typically done by computationally expensive MCMC methods in a single but trained generative pass. They could also be used to estimate partition functions and free energies, conditional probabilities of supersets (supergraphs) given a subset (subgraph), as well as marginal distributions over all supersets (supergraphs) of a given set (graph). We introduce variations enabling the estimation of entropy and mutual information, sampling from a Pareto frontier, connections to reward-maximizing policies, and extensions to stochastic environments, continuous actions and modular energy functions.

This paper presents results of a study of the performance of several base classifiers for recognition of handwritten characters of the modern Latin alphabet. Base classification performance is further enhanced by utilizing Viterbi error correction by determining the Viterbi sequence. Hidden Markov Models (HMMs) models exploit relationships between letters within a word to determine the most likely sequence of characters. Four base classifiers are studied along with eight feature sets extracted from the handwritten dataset. The best classification performance after correction was 89.8%, and the average was 68.1%

Particle filtering methods are widely applied in sequential state estimation within nonlinear non-Gaussian state space model. However, the traditional particle filtering methods suffer the weight degeneracy in the high-dimensional state space model. Currently, there are many methods to improve the performance of particle filtering in high-dimensional state space model. Among these, the more advanced method is to construct the Sequential Makov chian Monte Carlo (SMCMC) framework by implementing the Composite Metropolis-Hasting (MH) Kernel. In this paper, we proposed to discrete the Zig-Zag Sampler and apply the Zig-Zag Sampler in the refinement stage of the Composite MH Kernel within the SMCMC framework which is implemented the invertible particle flow in the joint draw stage. We evaluate the performance of proposed method through numerical experiments of the challenging complex high-dimensional filtering examples. Nemurical experiments show that in high-dimensional state estimation examples, the proposed method improves estimation accuracy and increases the acceptance ratio compared with state-of-the-art filtering methods.

This work aims to provide an engagement decision support tool for Beyond Visual Range (BVR) air combat in the context of Defensive Counter Air (DCA) missions. In BVR air combat, engagement decision refers to the choice of the moment the pilot engages a target by assuming an offensive stance and executing corresponding maneuvers. To model this decision, we use the Brazilian Air Force's Aerospace Simulation Environment (Ambiente de Simula\c{c}\~ao Aeroespacial - ASA in Portuguese), which generated 3,729 constructive simulations lasting 12 minutes each and a total of 10,316 engagements. We analyzed all samples by an operational metric called the DCA index, which represents, based on the experience of subject matter experts, the degree of success in this type of mission. This metric considers the distances of the aircraft of the same team and the opposite team, the point of Combat Air Patrol, and the number of missiles used. By defining the engagement status right before it starts and the average of the DCA index throughout the engagement, we create a supervised learning model to determine the quality of a new engagement. An algorithm based on decision trees, working with the XGBoost library, provides a regression model to predict the DCA index with a coefficient of determination close to 0.8 and a Root Mean Square Error of 0.05 that can furnish parameters to the BVR pilot to decide whether or not to engage. Thus, using data obtained through simulations, this work contributes by building a decision support system based on machine learning for BVR air combat.

This course is about the fundamental concepts of machine learning, focusing on regression, SVM, decision trees and neural networks. These topics are getting very hot nowadays because these learning algorithms can be used in several fields from software engineering to investment banking. Learning algorithms can recognize patterns which can help detect cancer for example or we may construct algorithms that can have a very good guess about stock prices movement in the market. In each section we will talk about the theoretical background for all of these algorithms then we are going to implement these problems together. We will use Python with SkLearn, Keras and TensorFlow.

Forecasting driving behavior or other sensor measurements is an essential component of autonomous driving systems. Often real-world multivariate time series data is hard to model because the underlying dynamics are nonlinear and the observations are noisy. In addition, driving data can often be multimodal in distribution, meaning that there are distinct predictions that are likely, but averaging can hurt model performance. To address this, we propose the Switching Recurrent Kalman Network (SRKN) for efficient inference and prediction on nonlinear and multi-modal time-series data. The model switches among several Kalman filters that model different aspects of the dynamics in a factorized latent state. We empirically test the resulting scalable and interpretable deep state-space model on toy data sets and real driving data from taxis in Porto. In all cases, the model can capture the multimodal nature of the dynamics in the data.

In recent times, deep neural networks achieved outstanding predictive performance on various classification and pattern recognition tasks. However, many real-world prediction problems have ordinal response variables, and this ordering information is ignored by conventional classification losses such as the multi-category cross-entropy. Ordinal regression methods for deep neural networks address this. One such method is the CORAL method, which is based on an earlier binary label extension framework and achieves rank consistency among its output layer tasks by imposing a weight-sharing constraint. However, while earlier experiments showed that CORAL's rank consistency is beneficial for performance, the weight-sharing constraint could severely restrict the expressiveness of a deep neural network. In this paper, we propose an alternative method for rank-consistent ordinal regression that does not require a weight-sharing constraint in a neural network's fully connected output layer. We achieve this rank consistency by a novel training scheme using conditional training sets to obtain the unconditional rank probabilities through applying the chain rule for conditional probability distributions. Experiments on various datasets demonstrate the efficacy of the proposed method to utilize the ordinal target information, and the absence of the weight-sharing restriction improves the performance substantially compared to the CORAL reference approach.

Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue by assessing DNNs' ability to estimate conditional probabilities and propose a framework for systematic uncertainty characterization. Denoting the input sample as x and the category as y, the classification task of assigning a category y to a given input x can be reduced to the task of estimating the conditional probabilities p(y|x), as approximated by the DNN at its last layer using the softmax function. Since softmax yields a vector whose elements all fall in the interval (0, 1) and sum to 1, it suggests a probabilistic interpretation to the DNN's outcome. Using synthetic and real-world datasets, we look into the impact of various factors, e.g., probability density f(x) and inter-categorical sparsity, on the precision of DNNs' estimations of p(y|x), and find that the likelihood probability density and the inter-categorical sparsity have greater impacts than the prior probability to DNNs' classification uncertainty.

The four essential chambers of one's heart that lie in the thoracic cavity are crucial for one's survival, yet ironically prove to be the most vulnerable. Cardiovascular disease (CVD) also commonly referred to as heart disease has steadily grown to the leading cause of death amongst humans over the past few decades. Taking this concerning statistic into consideration, it is evident that patients suffering from CVDs need a quick and correct diagnosis in order to facilitate early treatment to lessen the chances of fatality. This paper attempts to utilize the data provided to train classification models such as Logistic Regression, K Nearest Neighbors, Support Vector Machine, Decision Tree, Gaussian Naive Bayes, Random Forest, and Multi-Layer Perceptron (Artificial Neural Network) and eventually using a soft voting ensemble technique in order to attain as many correct diagnoses as possible.

We start by introducing a simple example to illustrate the kind of problems we are interested in solving. Consider the problem of estimating a parameter θ using data from a small experiment and a prior distribution constructed from similar previous experiments. The specific problem description is borrowed from [3]: Estimating the risk of tumor in a group of rats. In the evaluation of drugs for possible clinical application, studies are routinely performed on rodents. For a particular study drawn from the statistical literature, suppose the immediate aim is to estimate θ, the probability of tumor in a population of female laboratory rats of type'F344' that receive a zero dose of the drug (a control group). The data show that 4 out of 14 rats developed endometrial stromal polyps (a kind of tumor). Typically, the mean and standard deviation of underlying tumor risks are not available. Rather, historical data are available on previous experiments on similar groups of rats. In the rat tumor example, the historical data were in fact a set of observations of tumor incidence in 70 groups of rats (table 1).