Jonathan Huang

About Me

I am a postdoctoral fellow working in the Computer Science Department at Stanford University and am supported by an NSF/CRA CI (Computing Innovations) fellowship. I am a member of the Geometric Computation Group which is headed by Leonidas Guibas. I am also part of the recently started Lytics Lab, a multidisciplinary group focused on Learning Analytics.

I received a Ph.D. in Robotics from the School of Computer Science at Carnegie Mellon University in 2011. Before coming to CMU, I studied math (also) at Stanford University. And before Stanford, I attended Oakton High School in Vienna, Virginia, and for a time, also Lynbrook High School in San Jose, California.

Research Interests

I am a strong believer in doing research which is motivated by compelling applications, while being committed to pushing on core research problems in machine learning. My main research interests lie in designing computationally efficient probabilistic reasoning and learning algorithms which allow computers to deal with the uncertainty and complexity inherent in real world data. On the theoretical side of things, I am particularly interested in building and reasoning with distributions over complex combinatorial spaces. My dissertation research specifically focused on probabilistic reasoning and learning with permutation data, which arises in myriad applications such as modeling preference rankings over objects, tracking multiple moving objects with a sensor network, as well as disease progression analysis.

I am currently most excited about the rise of MOOCS (Massive Open Online Courses) such as Coursera and Udacity and how to make use of the massive amount of student data generated by these websites which log, among many other things, every video event, forum interaction, or homework attempt submitted by each student. Not surprisingly, there are a number of probabilistic reasoning problems and combinatorial data types which appear in the "MOOC-alytics" domain. With collaborators, I am working towards highly scalable methods that use cutting edge machine learning techniques for modeling student behavior and for providing automated, informative feedback for complex homework assignments. Finally, for your viewing pleasure, here is a wordle generated from abstracts of my papers:

Papers

• Tuned Models of Peer Assessment in MOOCs,
  Chris Piech, Jonathan Huang, Zhenghao Chen, Chuong Do, Andrew Ng, Daphne Koller.
  In Proceedings of The 6th International Conference on Educational Data Mining (EDM 2013),
  Memphis, TN, USA, July 2013.
  [pdf] [appendix] [abstract] [bibtex]
  
  Abstract:
  In massive open online courses (MOOCs), peer grading serves as a critical tool for scaling the grading of complex, open-ended assignments to courses with tens or hundreds of thousands of students. But despite promising initial trials, it does not always deliver accurate results compared to human experts. In this paper, we develop algorithms for estimating and correcting for grader biases and reliabilities, showing significant improvement in peer grading accuracy on real data with 63,199 peer grades from Coursera's HCI course offerings --- the largest peer grading networks analysed to date. We relate grader biases and reliabilities to other student factors such as student engagement, performance as well as commenting style. We also show that our model can lead to more intelligent assignment of graders to gradees.
  BibTeX Citation:
  @inproceedings{piech13,
  author = {Chris Piech and Jonathan Huang and Zhenghao Chen and Chuong Do and Andrew Ng and Daphne Koller},
  title = {Tuned Models of Peer Assessment in {MOOC}s},
  booktitle = {Proceedings of The 6th International Conference on Educational Data Mining (EDM 2013)},
  year = {2013}
  }
  
• Probabilistic Event Cascades for Alzheimer's Disease,
  Jonathan Huang, Daniel Alexander.
  In Advances in Neural Information Processing Systems (NIPS), 2012,
  Lake Tahoe, CA, USA, December 2012.
  [pdf] [poster] [abstract] [bibtex]
  
  Abstract:
  Accurate and detailed models of neurodegenerative disease progression such as Alzheimer's (AD) are crucially important for reliable early diagnosis and the determination of effective treatments. We introduce the ALPACA (Alzheimer's disease Probabilistic Cascades) model, a generative model linking latent Alzheimer's progression dynamics to observable biomarker data. In contrast with previous works which model disease progression as a fixed event ordering, we explicitly model the variability over such orderings among patients which is more realistic, particularly for highly detailed progression models. We describe efficient learning algorithms for ALPACA and discuss promising experimental results on a real cohort of Alzheimer's patients from the Alzheimer's Disease Neuroimaging Initiative.
  BibTeX Citation:
  @inproceedings{huang+al:nips12alpaca,
  title = {Probabilistic Event Cascades for Alzheimer's Disease},
  author = {Jonathan Huang and Daniel Alexander},
  booktitle = {In Advances in Neural Information Processing Systems (NIPS)},
  year = 2012,
  month = {December},
  address = {Lake Tahoe, CA, USA}
  }
  
• Riffled Independence for Efficient Inference with Partial Rankings,
  Jonathan Huang, Ashish Kapoor, Carlos Guestrin.
  Journal of Artificial Intelligence Research (JAIR).,
  Vol. 44 (2012), pages 491-532.
  [pdf] [abstract] [bibtex]
  
  Abstract:
  Distributions over rankings are used to model data in a multitude of real world settings such as preference analysis and political elections. Modeling such distributions presents several computational challenges, however, due to the factorial size of the set of rankings over an item set. Some of these challenges are quite familiar to the artificial intelligence community, such as how to compactly represent a distribution over a combinatorially large space, and how to efficiently perform probabilistic inference with these representations. With respect to ranking, however, there is the additional challenge of what we refer to as human task complexity users are rarely willing to provide a full ranking over a long list of candidates, instead often preferring to provide partial ranking information. Simultaneously addressing all of these challenges i.e., designing a compactly representable model which is amenable to efficient inference and can be learned using partial ranking data is a difficult task, but is necessary if we would like to scale to problems with nontrivial size. In this paper, we show that the recently proposed riffled independence assumptions cleanly and efficiently address each of the above challenges. In particular, we establish a tight mathematical connection between the concepts of riffled independence and of partial rankings. This correspondence not only allows us to then develop efficient and exact algorithms for performing inference tasks using riffled independence based represen- tations with partial rankings, but somewhat surprisingly, also shows that efficient inference is not possible for riffle independent models (in a certain sense) with observations which do not take the form of partial rankings. Finally, using our inference algorithm, we introduce the first method for learning riffled independence based models from partially ranked data.
  BibTeX Citation:
  @article{huangetal:jair12,
  title = {Riffled Independence for Efficient Inference with Partial Ranking},
  author = {Jonathan Huang and Ashish Kapoor and Carlos Guestrin},
  journal = {Journal of Artificial Intelligence},
  volume = {44},
  pages = {491-532},
  year = {2012},
  }
  
• Uncovering the Riffled Independence Structure of Ranked Data,
  Jonathan Huang, Carlos Guestrin.
  Electronic Journal of Statistics, Vol. 6 (2012) 1999-230.
  Communicated July 2010. (32 pages)
  [pdf] [long version (ArXiv)] [abstract] [bibtex]
  
  Abstract:
  Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called riffled independence, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. Within the context of ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. In this paper, we provide a formal introduction to riffled independence and propose an automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled independence.
  BibTeX Citation:
  @article{huangetal:ejs12,
  title = {Uncovering the Riffled Independence Structure of Ranked Data},
  author = {Jonathan Huang and Carlos Guestrin},
  journal = {Electronic Journal of Statistics},
  volume = {6},
  pages = {199-230},
  year = {2012},
  }
  
• Probabilistic Reasoning and Learning on Permutations: Exploiting Structural Decompositions of the Symmetric Group,
  Jonathan Huang.
  Doctoral Dissertation,
  Carnegie Mellon University, July 2011.
  [pdf] [defense slides] [abstract] [bibtex]
  
  Abstract:
      Probabilistic reasoning and learning with permutation data arises as a fundamental problem in myriad applications such as modeling preference rankings over objects (such as webpages), tracking multiple moving objects, reconstructing the temporal ordering of events from multiple imperfect accounts, and more. Since the number of permutations scales factorially with the number of objects being ranked or tracked, however, it is not feasible to represent and reason with arbitrary probability distributions on permutations. Consequently, many approaches to probabilistic reasoning problems on the group of permutations have been either ad-hoc, unscalable, and/or relied on rigid and unrealistic assumptions. For example, common factorized probability distribution representations, such as graphical models, are inefficient due to the mutual exclusivity constraints that are typically associated with permutations.
  
      This thesis addresses problems of scalability for probabilistic reasoning with permutations by exploiting a number of methods for decomposing complex distributions over permutations into simpler, smaller component parts. In particular, we explore two general and complementary approaches for decomposing distributions over permutations: (1) \emph{additive decompositions} and (2) \emph{multiplicative decompositions}. Our additive approach is based on the idea of projecting a distribution onto a group theoretic generalization of the Fourier basis. Our multiplicative approach assumes a factored form for the underlying probability distribution based on a generalization of the notion of probabilistic independence which we call \emph{riffled independence}.
  
       We show that both probabilistic decompositions lead to compact representations for distributions over permutations and that one can formulate efficient probabilistic inference algorithms by taking advantage of the combinatorial structure of each representation. An underlying theme throughout is the idea that both kinds of structural decompositions can be employed in tandem to relax the apparent intractability of probabilistic reasoning over the space of permutations.
  
       From the theoretical side, we address a number of problems in understanding the consequences of our approximations. For example, we present results in this thesis which illuminate the nature of error propagation in the Fourier domain and propose methods for mitigating their effects.
  
       Finally, we apply our decompositions to multiple application domains. For example, we show how the methods in the thesis can be used to solve challenging camera tracking scenarios as well as to reveal latent voting patterns and structure in Irish political elections and food preference surveys.
  
       To summarize, the main contributions of this thesis can be categorized into the following three broad categories:
    -Principled and compactly representable approximations of probability distributions over the group of permutations,
    -Flexible probabilistic reasoning and learning algorithms which exploit the structure of these compact representations for running time efficiency, and
    -Theoretical analyses of approximation quality as well as algorithmic and sample complexity.
  BibTeX Citation:
  @phdthesis{huang:thesis11,
  author = {Jonathan Huang},
  title = {Probabilistic Reasoning and Learning on Permutations: Exploiting Structural Decompositions of the Symmetric Group},
  school = {Carnegie Mellon University},
  year = {2011}
  }
• Efficient Probabilistic Inference with Partial Ranking Queries,
  Jonathan Huang, Ashish Kapoor, Carlos Guestrin.
  In The 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011) ,
  Barcelona, Spain, July 2011. (8 pages)
  [pdf] [proofs] [abstract] [bibtex]
  
  Abstract:
  Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or probabilistic independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical probabilistic queries. For ranking models, ``typical'' queries predominantly take the form of partial ranking queries (e.g., given a user's top-$k$ favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled independence factorizations proposed in recent literature are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.
  BibTeX Citation:
  @inproceedings{huangetal:uai11prank,
  title = {Efficient Probabilistic Inference with Partial Ranking Queries},
  author = {Jonathan Huang and Ashish Kapoor and Carlos Guestrin},
  booktitle = {The 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011)},
  month = {July},
  year = {2011},
  address = {Barcelona, Spain},
  }
  
• Fourier-Information Duality in the Identity Management Problem,
  Xiaoye Jiang, Jonathan Huang, Leonidas Guibas,
  In The European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML 2011) ,
  Athens, Greece, September 2011.
  [pdf] [abstract] [bibtex]
  Abstract:
  We compare two recently proposed approaches for representing probability distributions over the space of permutations in the context of multi-target tracking. We show that these two representations, the Fourier approximation and the information form approximation can both be viewed as low dimensional projections of a true distribution, but with respect to different metrics. We identify the strengths and weaknesses of each approximation, and propose an algorithm for converting between the two forms, allowing for a \emph{hybrid} approach that draws on the strengths of both representations. We show experimental evidence that there are situations where hybrid algorithms are favorable.
  BibTeX citation:
  @inproceedings{jiangetal11,
  title = {Fourier-Information Duality in the Identity Management Problem},
  author = {Xiaoye Jiang and Jonathan Huang and Leonidas Guibas},
  booktitle = {The European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML 2011)},
  month = {September},
  year = {2011},
  address = {Athens, Greece}
  }
  
• Learning Hierarchical Riffle Independent Groupings from Rankings,
  Jonathan Huang, Carlos Guestrin.
  In International Conference on Machine Learning (ICML 2010) ,
  Haifa, Israel, June 2010. (8 pages)
  [pdf] [proofs] [poster] [slides] [abstract] [bibtex]
  
  Abstract:
  Riffled independence is a generalized notion of probabilistic independence that has been shown to be naturally applicable to ranked data. In the riffled independence model, one assigns rankings to two disjoint sets of items independently, then in a second stage, interleaves (or riffles) the two rankings together to form a full ranking, as if by shuffling a deck of cards. Because of this interleaving stage, it is much more difficult to detect riffled independence than ordinary independence. In this paper, we provide the first automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled independence.
  BibTeX Citation:
  @inproceedings{huang+guestrin:icml10riffle,
  title = {Learning Hierarchical Riffle Independent Groupings from Rankings},
  author = {Jonathan Huang and Carlos Guestrin},
  booktitle = {International Conference on Machine Learning (ICML 2010)},
  month = {June},
  year = {2010},
  address = {Haifa, Israel},
  }
  
• Riffled Independence for Ranked Data,
  Jonathan Huang, Carlos Guestrin.
  In Advances in Neural Information Processing Systems (NIPS 2009) ,
  Vancouver, Canada, December 2009. (8 pages)
  [pdf] [spotlight] [audio] [proofs] [poster] [slides] [abstract] [bibtex]
  
  Abstract:
  Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called \emph{riffled independence}, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the \emph{riffle shuffle}, common in card games, to combine the two permutations to form a single permutation. In ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. We provide a formal introduction and present algorithms for using riffled independence within Fourier-theoretic frameworks which have been explored by a number of recent papers.
  BibTeX Citation:
  @inproceedings{huang+guestrin:nips09riffle,
  title = {Riffled Independence for Ranked Data},
  author = {Jonathan Huang and Carlos Guestrin},
  booktitle = {In Advances in Neural Information Processing Systems (NIPS)},
  month = {December},
  year = {2009},
  address = {Vancouver, Canada},
  }
  
• Fourier Theoretic Probabilistic Inference over Permutations ,
  Jonathan Huang, Carlos Guestrin, Leonidas Guibas.
  Journal of Machine Learning (JMLR), Volume 10
  pp. 997-1070, May 2009. (74 pages)
  [pdf] [abstract] [bibtex]
  
  Abstract:
  Permutations are ubiquitous in many real-world problems, such as voting, ranking, and data association. Representing uncertainty over permutations is challenging, since there are $n!$ possibilities, and typical compact and factorized probability distribution representations, such as graphical models, cannot capture the mutual exclusivity constraints associated with permutations. In this paper, we use the ``low-frequency'' terms of a Fourier decomposition to represent distributions over permutations compactly. We present \emph{Kronecker conditioning}, a novel approach for maintaining and updating these distributions directly in the Fourier domain, allowing for polynomial time bandlimited approximations. Low order Fourier-based approximations, however, may lead to functions that do not correspond to valid distributions. To address this problem, we present a quadratic program defined directly in the Fourier domain for projecting the approximation onto a relaxation of the polytope of legal marginal distributions. We demonstrate the effectiveness of our approach on a real camera-based multi-person tracking scenario.
  BibTeX Citation:
  @article{huang+al:jmlr09permdist,
  author = {Jonathan Huang and Carlos Guestrin and Leonidas Guibas},
  title = {Fourier Theoretic Probabilistic Inference over Permutations},
  journal = {Journal of Machine Learning Research (JMLR)},
  year = {2009},
  volume = {10},
  pages = {997-1070},
  month = {May},
  }
  
• Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems,
  Le Song, Jonathan Huang, Alex Smola, and Kenji Fukumizu.
  In International Conference on Machine Learning (ICML 2009)
  Montreal, Canada, June 2009. (8 pages)
  [pdf] [slides] [poster] [proofs] [abstract] [bibtex]
  
  Abstract:
  In this paper, we extend the Hilbert space embedding approach to handle conditional distributions. We derive a kernel estimate for the conditional embedding, and show its connection to ordinary embeddings. Conditional embeddings largely extend our ability to manipulate distributions in Hibert spaces, and as an example, we derive a nonparametric method for modeling dynamical systems where the belief state of the system is maintained as a conditional embedding. Our method is very general in terms of both the domains and the types of distributions that it can handle, and we demonstrate the effectiveness of our method in various dynamical systems. We expect that conditional embeddings will have wider applications beyond modeling dynamical systems.
  BibTeX Citation:
  @inproceedings{Song+al:icml2010hilbert,
  author = "Le Song and Jonathan Huang and Alex Smola and Kenji Fukumizu",
  title = "Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems",
  booktitle = "International Conference on Machine Learning (ICML 2009)",
  month = "June",
  year = "2009",
  }
  
• Exploiting Probabilistic Independence for Permutations ,
  Jonathan Huang, Carlos Guestrin, Xiaoye Jiang, and Leonidas Guibas.
  In Artificial Intelligence and Statistics (AISTATS 2009)
  Clearwater Beach, Florida USA, April 2009. (8 pages)
  [pdf] [slides] [proofs] [abstract] [bibtex]
  
  Abstract:
  Permutations are ubiquitous in many real world problems, such as voting, rankings and data association. Representing uncertainty over permutations is challenging, since there are $n!$ possibilities. Recent Fourier-based approaches can be used to provide a compact representation over low-frequency components of the distribution. Though polynomial, the complexity of these representations grows very rapidly, especially if we want to maintain reasonable estimates for peaked distributions. In this paper, we first characterize the notion of probabilistic independence for distributions over permutations. We then present a method for factoring distributions into independent components in the Fourier domain, and use our algorithms to decompose large problems into much smaller ones. We demonstrate that our method provides very significant improvements in terms of running time, on real tracking data.
  BibTeX Citation:
  @inproceedings{Huang+al:aistats09indep,
  title = {Exploiting Probabilistic Independence for Permutations},
  author = {Jonathan Huang and Carlos Guestrin and Xiaoye Jiang and Leonidas Guibas},
  booktitle = {In Artificial Intelligence and Statistics (AISTATS)},
  year = 2009,
  month = {April}
  }
  
• Efficient Inference for Distributions on Permutations ,
  Jonathan Huang, Carlos Guestrin, and Leonidas Guibas.
  In Advances in Neural Information Processing Systems (NIPS 2007) ,
  Vancouver, Canada, December 2007. (8 pages)
  Honorable Mention for Outstanding Student Paper.
  [pdf] [slides] [poster] [spotlight] [talk] [abstract] [bibtex]
  
  Abstract:
  Permutations are ubiquitous in many real world problems, such as voting, rankings and data association. Representing uncertainty over permutations is challenging, since there are $n!$ possibilities, and typical compact representations such as graphical models cannot efficiently capture the mutual exclusivity constraints associated with permutations. In this paper, we use the ``low-frequency'' terms of a Fourier decomposition to represent such distributions compactly. We present \emph{Kronecker conditioning}, a general and efficient approach for maintaining these distributions directly in the Fourier domain. Low order Fourier-based approximations can lead to functions that do not correspond to valid distributions. To address this problem, we present an efficient quadratic program defined directly in the Fourier domain to project the approximation onto a relaxed form of the marginal polytope. We demonstrate the effectiveness of our approach on a real camera-based multi-people tracking setting.
  BibTeX Citation:
  @inproceedings{Huang+al:nips07fourier,
  title = {Efficient Inference for Distributions on Permutations},
  author = {Jonathan Huang and Carlos Guestrin and Leonidas Guibas},
  booktitle = {In Advances in Neural Information Processing Systems (NIPS)},
  year = 2007,
  month = {December},
  address = {Vancouver, Canada},
  }
  
• A Database of Vocal Tract Resonance Trajectories for Research in Speech Processing
  Li Deng , Xiaodong Cui, Robert Pruvenok, Jonathan Huang, Safiyy Momen, Yanyi Chen, Abeer Alwan .
  In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006) ,
  Toulouse, France, May 2006, pp. 60-63. (4 pages)
  [pdf] [poster] [abstract] [bibtex]
  
  Abstract:
  While vocal tract resonances (VTRs, or formants that are defined as such resonances) are known to play a critical role in human speech perception and in computer speech processing, there has been a lack of standard databases needed for the quantitative evaluation of au- tomatic VTR extraction techniques. We report in this paper on our recent effort to create a publicly available database of the first three VTR frequency trajectories. The database contains a representative subset of the TIMIT corpus with respect to speaker, gender, dialect and phonetic context, with a total of 538 sentences. A Matlab-based labeling tool is developed, with high-resolution wideband spectro- grams displayed to assist in visual identification of VTR frequency values which are then recorded via mouse clicks and local spline in- terpolation. Special attention is paid to VTR values during consonant- to-vowel (CV) and vowel-to-consonant (VC) transitions, and to speech segments with vocal tract anti-resonances. Using this database, we quantitatively assess two common automatic VTR tracking tech- niques in terms of their average tracking errors analyzed within each of the six major broad phonetic classes as well as during CV and VC transitions. The potential use of the VTR database for research in several areas of speech processing is discussed.
  BibTeX Citation:
  @inproceedings{Deng06adatabase,
  author = {Li Deng and Xiaodong Cui and Robert Pruvenok and Jonathan Huang and Safiyy Momen and Yanyi Chen and Abeer Alwan},
  title = {A database of vocal tract resonance trajectories for research in speech processing},
  booktitle = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006)},
  year = {2006},
  pages = {60--63}
  }
  

Talks (online)

	Adaptive Fourier-Domain Inference on the Symmetric Group Algebraic Methods in Machine Learning Workshop, NIPS '08 Whistler, Canada
	Probability Distributions on Permutations: Compact Representations and Inference Machine Learning Lunch Seminar, 2008 Carnegie Mellon University
	Exploiting Independence and Its Generalizations for Reasoning about Permutation Data Machine Learning Lunch Seminar, 2010 Carnegie Mellon University

Teaching

• 16-831 (Statistical Techniques in Robotics), Fall '07
• 10-701 (Graduate Machine Learning), Spring '07

Code

• PyMallows
  Jonathan Huang
  Python routines for fitting and simulating from a generalized Mallows model. Learning algorithms implemented for both full and partial rankings
  [download] [readme]

• PROPS: Probabilistic Reasoning on Permutations toolbox
  Jonathan Leonard Long, Jonathan Huang,
  C++/Python library for reasoning/learning with distributions on permutations. (work in progress)
  [download] [documentation] [webpage]
• Littlewood-Richardson rule
  Jonathan Huang
  A matlab implementation of the Littlewood-Richardson rule.
  
  • enumeratelrtabs.m
  • lrtabvis.m
• (LDA) Latent Dirichlet Allocation
  Jonathan Huang and Tomasz Malisiewicz,
  An implementation of the mean field inference/learning algorithms from Blei et al. (2003)
  
  • ldainference.m
  • lda_param_est.m
  • trainLDA.m
  Sample output on 20 Newsgroups dataset: [Link]
• Matlab function for visualizing a 2d Dirichlet distribution,
  Jonathan Huang
• HLNfit,
  Jonathan Huang and Tomasz Malisiewicz,
  Code for fitting a Hierarchical Logistic Normal distribution.
  There is also a Romanian translation by Maxim Petrenko - Software blogger

Data

	Jigsaw Puzzle Data: [View][Download]
	Clebsch-Gordan series/coefficients (for the symmetric group): [Download]
	Manually labeled VTR-formant data from a subset of the TIMIT database: This database was created by a joint collaboration between MSR and UCLA (IPAM). See our ICASSP2006 paper (contained in the download) for details. Note that this is a 20MB download. We suggest that you save it in your disks before installing it. Note also that this is a database, although it appears as a program when you are running and "installing" it. [Download link]

Miscellaneous writeups, presentations... and art!

• I co-organized a NIPS 2009 workshop on Learning with Orderings with Tiberio Caetano, Carlos Guestrin, Risi Kondor, Guy Lebanon, and Marina Meila.
• "Bag of words" art installation at Gates-Hillman complex. (joint work with Khalid El-Arini, Sue Ann Hong, Joseph Gonzalez)
  [photos] [abstract]
  Abstract:
  Surprisingly, much of the meaning behind written language is preserved even when the ordering of the individual words is lost. Knowing only that a document contains the words "love" or "science" can reveal a great deal about its essence. Conversely, words such as "in," "the" and "of" reveal little. Computers use this simple idea to overcome their inability to understand language as humans do. The piece challenges the viewer to draw conclusions about a document without knowing the original order of the words.
• Tomasz Malisiewicz and I recently gave a tutorial on Learning and Inference in Vision: from Features to Scene Understanding at the MLD Student Research Symposium on November 13. [slides].
• Probabilistic Reasoning with Permutations: A Fourier-Theoretic Approach,
  Jonathan Huang,
  My thesis proposal document.
  [pdf] [slides] [abstract]
  Abstract:
     Permutations are ubiquitous in many real-world problems, such as voting, ranking, and data association. Representing uncertainty over permutations is challenging, since there are $n!$ possibilities, and common factorized probability distribution representations, such as graphical models, are inefficient due to the mutual exclusivity constraints that are typically associated with permutations.
     This thesis explores a new approach for probabilistic reasoning with permutations based on the idea of approximating distributions using their low-frequency Fourier components. We use a generalized Fourier transform defined for functions on permutations, but unlike the widely used Fourier analysis on the circle or the real line, Fourier transforms of functions on permutations take the form of ordered collections of matrices. As we show, maintaining the appropriate set of low-frequency Fourier terms corresponds to maintaining matrices of simple marginal probabilities which summarize the underlying distribution. We show how to derive the Fourier coefficients of a variety of probabilistic models which arise in practice and that many useful models are either well-approximated or exactly represented by low-frequency (and in many cases, sparse) Fourier coefficient matrices.
     In addition to showing that Fourier representations are both compact and intuitive, we show how to cast common probabilistic inference operations in the Fourier domain, including marginalization, conditioning on evidence, and factoring based on probabilistic independence. The algorithms presented in this thesis are fully general and work gracefully in \emph{bandlimited settings} where only a partial subset of Fourier coefficients is made available.
     From the theoretical side, we tackle several problems in understanding the consequences of the bandlimiting approximation. We present results in this thesis which illuminate the nature of error propagation in the Fourier domain and propose methods for mitigating their effects.
     Finally we demonstrate the effectiveness of our approach on several real datasets and show that our methods, in addition to being well-founded theoretically, are also scalable and provide superior results in practice.
• Hierarchical Logistic Normal parameter estimation,
  Jonathan Huang, Tomasz Malisiewicz,
  A project for Alyosha Efros's class on Learning based methods in computer vision. See our application to object recognition.
• Maximum Likelihood Estimation of Dirichlet Distributions ,
  Jonathan Huang,
  Notes on several ways to numerically find the MLE of a Dirichlet Distribution. This was done for a Math Fundamentals for Robotics course taught by Mike Erdmann.
• Sperner's Lemma ,
  Jonathan Huang,
  Some theorems/corollaries of Sperner's Lemma that I collected for a combinatorics class. Sperner is an easy combinatorial fact about labelings on a simplicial complex, but it has several surprising applications in topology and analysis. The famous Brouwer fixed point theorem, and the fundamental theorem of algebra are two of the examples that I discuss. [typos]
• Notes on the Kalman Filter ,
  Jonathan Huang,
  A derivation of the Kalman filter updates. The notes try to mostly follow the development given by Drew Bagnell in the Statistical Techniques for Robotics class at CMU.
• Cup Products in Computational Topology ,
  Jonathan Huang,
  Senior Honors Thesis (advisor: Gunnar Carlsson). We show an application of topological persistence to computing invariants related to the cohomology (cup product structure) of a finite simplicial complex.

Personal stuff/hobbies

	Garden of Weedin' (joint work w/Karl Goodman) Most people do not know this about me, but I have gardening on my list of former hobbies.
	Photorealistic rendering, Scientific visualization, and Computer games In a previous life, I was really interested in computer graphics. Actually I still am, but I never have time for it anymore.
	A poem I like =) (Shamelessly borrowed from Ravi Vakil from Stanford)
	Fishtank (joint work with Lucia Castellanos) We have 6 gouramis (1 blue, 2 gold, 3 kissing), 1 pleco, and 4 tiger barbs in a 30 gallon planted tank.