arXiv subjects

Roni Khardon

Publications and source records attributed to Roni Khardon.

24 records · Page 2Linked to original sources

arXiv2012

Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from all tasks. Therefore sparse solutions, that avoid using the entire data directly and instead use a set of informative "representatives" are desirable. The paper investigates this problem for the grouped mixed-effect GP model where each individual response is given by a fixed-effect, taken from one of a set of unknown groups, plus a random individual effect function that captures variations among individuals. Such models have been widely used in previous work but no sparse solutions have been developed. The paper presents the first sparse solution for such problems, showing how the sparse approximation can be obtained by maximizing a variational lower bound on the marginal likelihood, generalizing ideas from single-task Gaussian processes to handle the mixed-effect model as well as grouping. Experiments using artificial and real data validate the approach showing that it can recover the performance of inference with the full sample, that it outperforms baseline methods, and that it outperforms state of the art sparse solutions for other multi-task GP formulations.

cs.LG↗

arXiv2012

Policy Iteration for Relational MDPs

Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the value iteration algorithm. However, exact versions of more complex algorithms, including policy iteration, have not been developed or analyzed. The paper investigates this potential and makes several contributions. First we observe two anomalies for relational representations showing that the value of some policies is not well defined or cannot be calculated for restricted representation schemes used in the literature. On the other hand, we develop a variant of policy iteration that can get around these anomalies. The algorithm includes an aspect of policy improvement in the process of policy evaluation and thus differs from the original algorithm. We show that despite this difference the algorithm converges to the optimal policy.

cs.AI↗

arXiv2012

Nonparametric Bayesian Estimation of Periodic Functions

Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the problem of identifying the period: estimating the period of a periodic function based on noisy observations made at irregularly spaced time points. This problem is still a difficult challenge despite extensive study in different disciplines. The paper makes several contributions toward solving this problem. First, we present a nonparametric Bayesian model for period finding, based on Gaussian Processes (GP), that does not make strong assumptions on the shape of the periodic function. As our experiments demonstrate, the new model leads to significantly better results in period estimation when the target function is non-sinusoidal. Second, we develop a new algorithm for parameter optimization for GP which is useful when the likelihood function is very sensitive to the setting of the hyper-parameters with numerous local minima, as in the case of period estimation. The algorithm combines gradient optimization with grid search and incorporates several mechanisms to overcome the high complexity of inference with GP. Third, we develop a novel approach for using domain knowledge, in the form of a probabilistic generative model, and incorporate it into the period estimation algorithm. Experimental results on astrophysics data validate our approach showing significant improvement over the state of the art in this domain.

cs.LG↗

arXiv2011

A Refined QSO Selection Method Using Diagnostics Tests: 663 QSO Candidates in the LMC

We present 663 QSO candidates in the Large Magellanic Cloud (LMC) selected using multiple diagnostics. We started with a set of 2,566 QSO candidates from our previous work selected using time variability of the MACHO LMC lightcurves. We then obtained additional information for the candidates by crossmatching them with the Spitzer SAGE, the MACHO UBVI, the 2MASS, the Chandra and the XMM catalogs. Using this information, we specified six diagnostic features based on mid-IR colors, photometric redshifts using SED template fitting, and X-ray luminosities in order to further discriminate high confidence QSO candidates in the absence of spectra information. We then trained a one-class SVM (Support Vector Machine) model using the diagnostics features of the confirmed 58 MACHO QSOs. We applied the trained model to the original candidates and finally selected 663 high confidence QSO candidates. Furthermore, we crossmatched these 663 QSO candidates with the newly confirmed 144 QSOs and 275 non-QSOs in the LMC fields. On the basis of the counterpart analysis, we found that the false positive rate is less than 1%.

astro-ph.CO↗

arXiv2011

First Order Decision Diagrams for Relational MDPs

Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational structure that can be naturally described in terms of objects and relations among them. Two contributions are presented. First, the paper develops First Order Decision Diagrams (FODD), a new compact representation for functions over relational structures, together with a set of operators to combine FODDs, and novel reduction techniques to keep the representation small. Second, the paper shows how FODDs can be used to develop solutions for RMDPs, where reasoning is performed at the abstract level and the resulting optimal policy is independent of domain size (number of objects) or instantiation. In particular, a variant of the value iteration algorithm is developed by using special operations over FODDs, and the algorithm is shown to converge to the optimal policy.

cs.AI↗

arXiv2011

QSO Selection Algorithm Using Time Variability and Machine Learning: Selection of 1,620 QSO Candidates from MACHO LMC Database

We present a new QSO selection algorithm using a Support Vector Machine (SVM), a supervised classification method, on a set of extracted times series features including period, amplitude, color, and autocorrelation value. We train a model that separates QSOs from variable stars, non-variable stars and microlensing events using 58 known QSOs, 1,629 variable stars and 4,288 non-variables using the MAssive Compact Halo Object (MACHO) database as a training set. To estimate the efficiency and the accuracy of the model, we perform a cross-validation test using the training set. The test shows that the model correctly identifies ~80% of known QSOs with a 25% false positive rate. The majority of the false positives are Be stars. We applied the trained model to the MACHO Large Magellanic Cloud (LMC) dataset, which consists of 40 million lightcurves, and found 1,620 QSO candidates. During the selection none of the 33,242 known MACHO variables were misclassified as QSO candidates. In order to estimate the true false positive rate, we crossmatched the candidates with astronomical catalogs including the Spitzer Surveying the Agents of a Galaxy's Evolution (SAGE) LMC catalog and a few X-ray catalogs. The results further suggest that the majority of the candidates, more than 70%, are QSOs.

astro-ph.IM↗