Graphical Models, Exponential Families, and Variational Inference

Wainwright, Martin J.; Jordan, Michael I.

doi:10.1561/2200000001

Cited by 2,181 publications

(2,524 citation statements)

References 156 publications

(350 reference statements)

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“…Preliminary experimentation with exponential models [Wainwright and Jordan 2003], where the output space was designed to be compatible to the above constraint gave mediocre results. We therefore turned to classification algorithms, which produce classifiers that score each candidate base in isolation, without explicitly assigning a natural base to a model.…”

Section: Assessment Function Learningmentioning

confidence: 99%

Upright orientation of man-made objects

Cohen–Or

Dror

et al. 2008

ACM SIGGRAPH 2008 Papers

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Humans usually associate an upright orientation with objects, placing them in a way that they are most commonly seen in our surroundings. While it is an open challenge to recover the functionality of a shape from its geometry alone, this paper shows that it is often possible to infer its upright orientation by analyzing its geometry. Our key idea is to reduce the two-dimensional (spherical) orientation space to a small set of orientation candidates using functionality-related geometric properties of the object, and then determine the best orientation using an assessment function of several functional geometric attributes defined with respect to each candidate. Specifically we focus on obtaining the upright orientation for man-made objects that typically stand on some flat surface (ground, floor, table, etc.), which include the vast majority of objects in our everyday surroundings. For these types of models orientation candidates can be defined according to static equilibrium. For each candidate, we introduce a set of discriminative attributes linking shape to function. We learn an assessment function of these attributes from a training set using a combination of Random Forest classifier and Support Vector Machine classifier. Experiments demonstrate that our method generalizes well and achieves about 90% prediction accuracy for both a 10-fold cross-validation over the training set and a validation with an independent test set.

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Section: Assessment Function Learningmentioning

confidence: 99%

Upright orientation of man-made objects

Cohen–Or

Dror

et al. 2008

ACM SIGGRAPH 2008 Papers

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show abstract

“…In the EM framework, unobserved data H are considered in addition to the observed data V , and it is supposed that the joint distribution, p(V , H | Θ), is in the exponential family [19]. Namely, there exist vector-valued or matrix-valued functions, S(·) and G(·), such that…”

Section: Em Algorithm Revisitedmentioning

confidence: 99%

Mutual Kernel Matrix Completion

Rivero

Lemence

Kato³

2017

IEICE Trans. Inf. & Syst.

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SUMMARYWith the huge influx of various data nowadays, extracting knowledge from them has become an interesting but tedious task among data scientists, particularly when the data come in heterogeneous form and have missing information. Many data completion techniques had been introduced, especially in the advent of kernel methods-a way in which one can represent heterogeneous data sets into a single form: as kernel matrices. However, among the many data completion techniques available in the literature, studies about mutually completing several incomplete kernel matrices have not been given much attention yet. In this paper, we present a new method, called Mutual Kernel Matrix Completion (MKMC) algorithm, that tackles this problem of mutually inferring the missing entries of multiple kernel matrices by combining the notions of data fusion and kernel matrix completion, applied on biological data sets to be used for classification task. We first introduced an objective function that will be minimized by exploiting the EM algorithm, which in turn results to an estimate of the missing entries of the kernel matrices involved. The completed kernel matrices are then combined to produce a model matrix that can be used to further improve the obtained estimates. An interesting result of our study is that the E-step and the M-step are given in closed form, which makes our algorithm efficient in terms of time and memory. After completion, the (completed) kernel matrices are then used to train an SVM classifier to test how well the relationships among the entries are preserved. Our empirical results show that the proposed algorithm bested the traditional completion techniques in preserving the relationships among the data points, and in accurately recovering the missing kernel matrix entries. By far, MKMC offers a promising solution to the problem of mutual estimation of a number of relevant incomplete kernel matrices. key words: kernel matrix completion, EM algorithm, Kullback-Leibler divergence, support vector machine (SVM), data fusion

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“…Properties of regular covers have been previously exploited in developing efficient database representation schemes (see Beeri et al (1983)), in approximating high-dimensional probability distributions (see Chow and Liu (1968)), in developing tractable semidefinite relaxations in sparse polynomial optimization problems (see Lasserre (2006)) and in developing efficient inference algorithms in probabilistic graphical models (see Wainwright and Jordan (2008)). In this paper, we use the structure of regular covers in distributionally robust optimization problems.…”

Section: Regular Covermentioning

confidence: 99%

Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals

Doan

Natarajan

2015

Operations Research

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In this paper, we develop a distributionally robust portfolio optimization model where the robustness is across different dependency structures among the random losses. For a Fréchet class of discrete distributions with overlapping marginals, we show that the distributionally robust portfolio optimization problem is efficiently solvable with linear programming. To guarantee the existence of a joint multivariate distribution consistent with the overlapping marginal information, we make use of a graph theoretic property known as the running intersection property. Building on this property, we develop a tight linear programming formulation to find the optimal portfolio that minimizes the worst-case Conditional Value-at-Risk measure. Lastly, we use a data-driven approach with financial return data to identify the Fréchet class of distributions satisfying the running intersection property and then optimize the portfolio over this class of distributions. Numerical results in two different datasets show that the distributionally robust portfolio optimization model improves on the sample-based approach

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Graphical Models, Exponential Families, and Variational Inference

Cited by 2,181 publications

References 156 publications

Upright orientation of man-made objects

Upright orientation of man-made objects

Mutual Kernel Matrix Completion

Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals

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