Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate it. Monte Carlo simulation is an effective technique that can be used to approximate the probability that a player will win and or tie a hand. However, without the use of a memory-intensive lookup table or a supercomputer, it becomes infeasible to run millions of times when training an agent with self-play. To combat the space-time tradeoff, we use deep learning to approximate the probabilities obtained from the Monte Carlo simulation with high accuracy. The learned model proves to be a lightweight alternative to Monte Carlo simulation, which ultimately allows us to use the probabilities as inputs during self-play efficiently. The source code and optimized neural network can be found at this https URL
Another paper used a Support Vector Machine (SVM) classifier to determine whether or not you will win the hand. They then used the confidence score from the classifier as an estimate of the probability of winning @cite_3 . Even though they showed that their classifier achieved precision of $>60
@cite_3
2089394015 1537017777 2169384781 2952550066
The support vector machine (SVM) has been widely applied for classification problems in both machine learning and statistics. Despite its popularity, however, SVM has some drawbacks in certain situations. In particular, the SVM classifier can be very sensitive to outliers in the training sample. Moreover, the number of support vectors (SVs) can be very large in many applications. To circumvent these drawbacks, we propose the robust truncated hinge loss SVM (RSVM), which uses a truncated hinge loss. The RSVM is shown to be more robust to outliers and to deliver more accurate classifiers using a smaller set of SVs than the standard SVM. Our theoretical results show that the RSVM is Fisher-consistent, even when there is no dominating class, a scenario that is particularly challenging for multicategory classification. Similar results are obtained for a class of margin-based classifiers. Support vector machines (SVM) is originally designed for binary classification. To extend it to multi-class scenario, a typical conventional way is to decompose an M-class problem into a series of two-class problems, for which one-against-all is the earliest and one of the most widely used implementations. However, certain theoretical analysis reveals a drawback, i.e., the competence of each classifier is totally neglected when the results of classification from the multiple classifiers are combined for the final decision. To overcome this limitation, this paper introduces reliability measures into the multi-class framework. Two measures are designed: static reliability measure (SRM) and dynamic reliability measure (DRM). SRM works on a collective basis and yields a constant value regardless of the location of the test sample. DRM, on the other hand, accounts for the spatial variation of the classifier's performance. Based on these two reliability measures, a new decision strategy for the one-against-all method is proposed, which is tested on benchmark data sets and demonstrates its effectiveness. We study the use of support vector machines (SVM) in classifying e-mail as spam or nonspam by comparing it to three other classification algorithms: Ripper, Rocchio, and boosting decision trees. These four algorithms were tested on two different data sets: one data set where the number of features were constrained to the 1000 best features and another data set where the dimensionality was over 7000. SVM performed best when using binary features. For both data sets, boosting trees and SVM had acceptable test performance in terms of accuracy and speed. However, SVM had significantly less training time. The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions centred on a subset of the training data, known as support vectors. Despite its widespread success, the SVM suffers from some important limitations, one of the most significant being that it makes point predictions rather than generating predictive distributions. Recently Tipping (1999) has formulated the Relevance Vector Machine (RVM), a probabilistic model whose functional form is equivalent to the SVM. It achieves comparable recognition accuracy to the SVM, yet provides a full predictive distribution, and also requires substantially fewer kernel functions. The original treatment of the RVM relied on the use of type II maximum likelihood (the evidence framework') to provide point estimates of the hyperparameters which govern model sparsity. In this paper we show how the RVM can be formulated and solved within a completely Bayesian paradigm through the use of variational inference, thereby giving a posterior distribution over both parameters and hyperparameters. We demonstrate the practicality and performance of the variational RVM using both synthetic and real world examples.