相关论文: Learning Deterministic Regular Expressions for the…

This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary $\Phi\in…

Noisy $k$-XOR is a basic average-case inference problem in which one observes random noisy $k$-ary parity constraints and seeks to recover, or more weakly, detect, a hidden Boolean assignment. A central question is to characterize the…

We give an active learning algorithm for deterministic one-counter automata (DOCAs) where the learner can ask the teacher membership and minimal equivalence queries. The algorithm called OL* learns a DOCA in time polynomial in the size of…

A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…

We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…

Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on…

Decision diagrams (DDs) have emerged as a state-of-the-art method for exact multiobjective integer linear programming. When the DD is too large to fit into memory or the decision-maker prefers a fast approximation to the Pareto frontier,…

In this paper we derive sufficient conditions for the convergence of two popular alternating minimisation algorithms for dictionary learning - the Method of Optimal Directions (MOD) and Online Dictionary Learning (ODL), which can also be…

Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search…

This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is…

Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…

A regular expression specifies a set of strings formed by single characters combined with concatenation, union, and Kleene star operators. Given a regular expression $R$ and a string $Q$, the regular expression matching problem is to decide…

We consider the question of learning the natural parameters of a $k$ parameter minimal exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the…

To address the challenges of reliable statistical inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via…

In this paper, we address the problem of discriminative dictionary learning (DDL), where sparse linear representation and classification are combined in a probabilistic framework. As such, a single discriminative dictionary and linear…

We present a polynomial time algorithm that constructs a deterministic parity automaton (DPA) from a given set of positive and negative ultimately periodic example words. We show that this algorithm is complete for the class of…

Designing short DNA words is a problem of constructing a set (i.e., code) of n DNA strings (i.e., words) with the minimum length such that the Hamming distance between each pair of words is at least k and the n words satisfy a set of…

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder…

We present a data structure that we call a Dynamic Representative Set. In its most basic form, it is given two parameters $0< k < n$ and allows us to maintain a representation of a family $\mathcal{F}$ of subsets of $\{1,\ldots,n\}$. It…

We consider processing an n x d matrix A in a stream with row-wise updates according to a recent algorithm called Frequent Directions (Liberty, KDD 2013). This algorithm maintains an l x d matrix Q deterministically, processing each row in…