Bayesian Inference
Activity Recognition: Linking Low-Level Sensors to High-Level Intelligence
Yang, Qiang (Hong Kong Hong Kong University of Science and Technology)
Sensors provide computer systems with a window to the outside world. Activity recognition "sees" what is in the window to predict the locations, trajectories, actions, goals and plans of humans and objects. Building an activity recognition system requires a full range of interaction from statistical inference on lower level sensor data to symbolic AI at higher levels, where prediction results and acquired knowledge are passed up each level to form a knowledge food chain. In this article, I will give an overview of some of the current activity recognition research works and explore a life-cycle of learning and inference that allows the lowest-level radio-frequency signals to be transformed into symbolic logical representations for AI planning, which in turn controls the robots or guides human users through a sensor network, thus completing a full life-cycle of knowledge.
Speeding Up Exact Solutions of Interactive Dynamic Influence Diagrams Using Action Equivalence
Zeng, Yifeng (Aalborg University) | Doshi, Prashant
Interactive dynamic influence diagrams (I-DIDs) are graphical models forย sequentialย decision makingย inย partially observableย settings sharedย by otherย agents.ย Algorithmsย for solvingย I-DIDsย face the challengeย of anย exponentiallyย growing spaceย of candidateย models ascribed toย other agents, over time. Previousย approach for exactly ย solving I-DIDs groups togetherย models having similar solutions into behaviorallyย equivalentย classesย andย updates theseย classes.ย ย We present aย new method that, in additionย to aggregating behaviorally equivalentย models, further groupsย models thatย prescribe identical actions at a single time step. We show how to update these augmented classesย and proveย thatย ourย method isย exact.ย ย The newย approach ย enables us to bound the aggregated model space by the cardinality of ย otherย agents'ย actions. Weย evaluateย itsย performance andย provide ย empirical results in support.
Semi-Supervised Classification using Sparse Gaussian Process Regression
Patel, Amrish (Indian Institute of Science) | Sundararajan, S. (Yahoo! Labs) | Shevade, Shirish (Indian Institute of Science)
Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.
Semi-Supervised Classification using Sparse Gaussian Process Regression
Patel, Amrish (Indian Institute of Science) | Sundararajan, S. (Yahoo! Labs) | Shevade, Shirish (Indian Institute of Science)
Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.
Semi-Supervised Classification using Sparse Gaussian Process Regression
Patel, Amrish (Indian Institute of Science) | Sundararajan, S. (Yahoo! Labs) | Shevade, Shirish (Indian Institute of Science)
Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.
Semi-Supervised Classification using Sparse Gaussian Process Regression
Patel, Amrish (Indian Institute of Science) | Sundararajan, S. (Yahoo! Labs) | Shevade, Shirish (Indian Institute of Science)
Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.
Semi-Supervised Classification using Sparse Gaussian Process Regression
Patel, Amrish (Indian Institute of Science) | Sundararajan, S. (Yahoo! Labs) | Shevade, Shirish (Indian Institute of Science)
Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.
Semi-Supervised Classification using Sparse Gaussian Process Regression
Patel, Amrish (Indian Institute of Science) | Sundararajan, S. (Yahoo! Labs) | Shevade, Shirish (Indian Institute of Science)
Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.
Conditional Probability Tree Estimation Analysis and Algorithms
Beygelzimer, Alina, Langford, John, Lifshits, Yuri, Sorkin, Gregory, Strehl, Alex
We consider the problem of estimating the conditional probability of a label in time $O(\log n)$, where $n$ is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Motivated by this analysis, we propose the first online algorithm which provably constructs a logarithmic depth tree on the set of labels to solve this problem. We test the algorithm empirically, showing that it works succesfully on a dataset with roughly $10^6$ labels.
Characterizing predictable classes of processes
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure $\mu$ belongs to an arbitrary class $\C$ of stochastic processes. We are interested in predictors $\rho$ whose conditional probabilities converge to the "true" $\mu$-conditional probabilities if any $\mu\in\C$ is chosen to generate the data. We show that if such a predictor exists, then a predictor can also be obtained as a convex combination of a countably many elements of $\C$. In other words, it can be obtained as a Bayesian predictor whose prior is concentrated on a countable set. This result is established for two very different measures of performance of prediction, one of which is very strong, namely, total variation, and the other is very weak, namely, prediction in expected average Kullback-Leibler divergence.