Related papers: Derivatives of Approximate Regular Expressions
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
The Word Error Rate (WER) is the common measure of accuracy for Automatic Speech Recognition (ASR). Transcripts are usually pre-processed by substituting specific characters to account for non-semantic differences. As a result of this…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Regularization of neural machine translation is still a significant problem, especially in low-resource settings. To mollify this problem, we propose regressing word embeddings (ReWE) as a new regularization technique in a system that is…
This paper presents a novel algorithm to obtain the closed-form anti-derivative of a function using Deep Neural Network architecture. In the past, mathematicians have developed several numerical techniques to approximate the values of…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
Matrix permanent plays a key role in data association probability calculations. Exact algorithms (such as Ryser's) scale exponentially with matrix size. Fully polynomial time randomized approximation schemes exist but are quite complex.…
Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
The non-linear sewing lemma constructs flows of rough differential equations from a braod class of approximations called almost flows. We consider a class of almost flows that could be approximated by solutions of ordinary differential…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
How to improve discriminative feature learning is central in classification. Existing works address this problem by explicitly increasing inter-class separability and intra-class similarity, whether by constructing positive and negative…
Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular…
We propose a hierarchy for approximate inference based on the Dobrushin, Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms, such as belief propagation, and also motivates novel algorithms such as factorized…
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…