### <NEWS>

And once the storm is over you won't remember how you made it through, how you managed to survive. You won't even be sure, in fact, whether the storm is really over. But one thing is certain. When you come out of the storm you won't be the same person who walked in. That's what this storm's all about.''

-Haruki Murakami

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##### THE OFFICIAL GOLDEN DOODLE OF UM

During an afternoon of Patrick and Oliver playing fetch with Patrick's dog Butters, Butters was recorded in a video that is slated for use in offial promotion for the University of Montana.

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##### COBRE GRANT AWARD

The Serang Lab has been awarded a COBRE grant. This grant will be used to hire UM graduate students to build new graphical models for two cutting-edge problems from computational biology.

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##### UM PILOT PROJECT GRANT AWARD

The University of Montana has awarded the Serang Lab a pilot project grant. This grant will fund a UM computer science student to work on an exciting project developing EvergreenForest, a new graphical models library.

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##### THE LAUNCH OF EXPLORING SCIENTIFIC WILDERNESS

Exploring Scientific Wilderness is a new podcast miniseries with short and sweet pieces of scientific brain candy.

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##### EVERGREENFOREST INFERENCE ENGINE 0.9

After years of work, the beta version of EvergreenForest has been released! It includes a fast, lazy implementation of trimmed convolution trees, a fast in-house FFT written in C++11 (using the lab's work on methods for performing bit-reversed permutation), and lots of other Waldmeister-flavored goodies to activate your almonds.

You can read more about it and download it here.

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##### THE INVENTION OF TRIMMED'' CONVOLUTION TREES

Trimmed convolution trees use sparsity in the solution space exploit sparsity in the input priors and likelihood of a convolution tree to achieve an algorithmic and practical speedup. For example, when all input priors are $$X_i \in \{0,1\}$$ and the likelihood $$Y=X_1 + X_2 + \cdots X_n \in \{0,1\},$$ all posteriors can be solved with trimmed convolution trees in $$O(n)$$ rather than the $$O(n \log(n) \log(n))$$ required by non-trimmed convolution trees.

Trimmed convolution trees generalize this to use narrower priors and likelihoods, even when some priors have larger support than others or when the likelihood distribution has are larger support than all priors, smaller support, or anything, making the first method $$\in o(nk \log(nk) \log(n))$$ on some problems with $$n$$ inputs each with $$k$$ bins.

The paper (in review) includes a demo that uses trimmed convolution trees to estimate posterior probabilities for peoples' orders given their total ice cream bill; the demo is, of course, written using the menu from Missoula's own Big Dipper Ice Cream.

The paper draft can be read here.

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##### FAST C++11 METHODS FOR BIT-REVERSED PERMUATION

The bit-reversed permutation is an important task for implementing an in-place FFT library. This paper explores several bit reversal methods on the x86 architecture, including new bit twiddling tricks and a proposed template-recursive, cache-oblivious method, which achieves state-of-the-art performance.

The paper draft can be found here. The repository (linked in the paper) includes translations in the mother tongue of each student who participated (Chinese, German, Turkish, and Spanish) to help students throughout the world participate in the joy of scientific computing. So when someone says, Bit reversal? How?'' you can say, 很好!''

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##### A FASTER, SIMPLER MULTIDIMENSIONAL ARRAY LIBRARY IN C++11

Florian Heyl, who is doing his masters Praktikum in the group, has just had his first paper accepted for publication. The paper (Heyl & Serang 2017, PROGRAMMING) introduces and benchmarks the template-recursive iteration over tensors'' (TRIOT) design pattern in C++11. The method enables easy vectorizing over tensors of different shaps and does not require tensor dimensions to be fixed at compile time.

Download the free header-only library here.

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##### MORE ACCURATE NUMERIC P-CONVOLUTION

The lab's second paper on the topic (Pfeuffer & Serang 2016, Journal of Machine Learning Research) builds upon the original idea, looking at the curve of (modeled using orthogonal polynomials) of a constant number of $$L_p$$ spaces. The way that these spaces bend toward the true maximum can allow us to estimate the maximum better than any particular numerically stable p-norm.

The paper highlights the approach with faster prediction of U.S. unemployment given S&P 500 index data (via a fast Viterbi path computation).

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##### THE INVENTION OF FAST NUMERIC MAX-CONVOLUTION

Max-convolution, a cousin of standard convolution but on the semiring $$( \times, \max )$$ (consider multiplying two polynomials but taking the maximum coefficient for every term rather than the sum of coefficients for that term), arises frequently in combinatorics and in Bayesian inference. In 2006, Bremner et al. discovered the first solution $$\in o(n^2);$$ theirs is a beautiful method, but it's only slightly sub-quadratic and relies on a reduction to APSP, and it is not fast enough for large-scale use in Bayesian networks. However, this problem can be approximated numerically by using $$L_p$$ space, where FFT can be used in $$\in O(n \log(n))$$ (Serang 2015, Journal of Computational Biology). The method can also be used to improve hidden Markov models (HMMs) with with k states from $$O(k^2 n)$$ to $$O(k \log(k)~ n),$$ whenever the transition matrix is a Toeplitz matrix.

Combined with the probabilistic convolution tree, the method can be used for max-product inverence when $$Y = X_1 + X_2 + \cdots + X_n.$$ This can be used to solve a generalization of the knapsack problem on integer-discretized supports.

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##### A FASTER DYNAMIC PROGRAMMING ALGORITHM

The probabilistic convolution tree (Serang 2014, PLOS ONE) is a new dynamic programming algorithm that solves a class of probabilistic problems, which are equivalent to a generalization of subset-sum on integer-discretized supports. When $$Y = X_1 + X_2 + \cdots + X_n$$ and each $$X_i \in \{0, 1, \ldots k-1\}$$ it computes all marginals simultaneously with a runtime $$\in O(n k \log(n k) \log(n)).$$

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