1,360 research outputs found
Typable Fragments of Polynomial Automatic Amortized Resource Analysis
Being a fully automated technique for resource analysis, automatic amortized resource analysis (AARA) can fail in returning worst-case cost bounds of programs, fundamentally due to the undecidability of resource analysis. For programmers who are unfamiliar with the technical details of AARA, it is difficult to predict whether a program can be successfully analyzed in AARA. Motivated by this problem, this article identifies classes of programs that can be analyzed in type-based polynomial AARA. Firstly, it is shown that the set of functions that are typable in univariate polynomial AARA coincides with the complexity class PTime. Secondly, the article presents a sufficient condition for typability that axiomatically requires every sub-expression of a given program to be polynomial-time. It is proved that this condition implies typability in multivariate polynomial AARA under some syntactic restrictions
A Simple and Scalable Static Analysis for Bound Analysis and Amortized Complexity Analysis
We present the first scalable bound analysis that achieves amortized
complexity analysis. In contrast to earlier work, our bound analysis is not
based on general purpose reasoners such as abstract interpreters, software
model checkers or computer algebra tools. Rather, we derive bounds directly
from abstract program models, which we obtain from programs by comparatively
simple invariant generation and symbolic execution techniques. As a result, we
obtain an analysis that is more predictable and more scalable than earlier
approaches. Our experiments demonstrate that our analysis is fast and at the
same time able to compute bounds for challenging loops in a large real-world
benchmark. Technically, our approach is based on lossy vector addition systems
(VASS). Our bound analysis first computes a lexicographic ranking function that
proves the termination of a VASS, and then derives a bound from this ranking
function. Our methodology achieves amortized analysis based on a new insight
how lexicographic ranking functions can be used for bound analysis
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Exponential Family Embeddings
Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. Exponential family embeddings extend the idea of word embeddings to other types of high-dimensional data. Exponential family embeddings have three ingredients; embeddings as latent variables, a predefined conditioning set for each observation called the context and a conditional likelihood from the exponential family. The embeddings are inferred with a scalable algorithm. This thesis highlights three advantages of the exponential family embeddings model class: (A) The approximations used for existing methods such as word2vec can be understood as a biased stochastic gradients procedure on a specific type of exponential family embedding model --- the Bernoulli embedding. (B) By choosing different likelihoods from the exponential family we can generalize the task of learning distributed representations to different application domains. For example, we can learn embeddings of grocery items from shopping data, embeddings of movies from click data, or embeddings of neurons from recordings of zebrafish brains. On all three applications, we find exponential family embedding models to be more effective than other types of dimensionality reduction. They better reconstruct held-out data and find interesting qualitative structure. (C) Finally, the probabilistic modeling perspective allows us to incorporate structure and domain knowledge in the embedding space. We develop models for studying how language varies over time, differs between related groups of data, and how word usage differs between languages. Key to the success of these methods is that the embeddings share statistical information through hierarchical priors or neural networks. We demonstrate the benefits of this approach in empirical studies of Senate speeches, scientific abstracts, and shopping baskets
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