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We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…
In this letter, we propose a novel computationally efficient coupled dictionary learning method that enforces pairwise correlation between the atoms of dictionaries learned to represent the underlying feature spaces of two different…
It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent…
Bilingual Lexicon Induction is the task of learning word translations without bilingual parallel corpora. We model this task as a matrix completion problem, and present an effective and extendable framework for completing the matrix. This…
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in…
An algorithm for numerically computing the exponential of a matrix is presented. We have derived a polynomial expansion of $e^x$ by computing it as an initial value problem using a symbolic programming language. This algorithm is shown to…
We present a supervised neural network model for polyphonic piano music transcription. The architecture of the proposed model is analogous to speech recognition systems and comprises an acoustic model and a music language model. The…
We describe a polynomial network technique developed for learning to classify clinical electroencephalograms (EEGs) presented by noisy features. Using an evolutionary strategy implemented within Group Method of Data Handling, we learn…
Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…
In a sparse representation based recognition scheme, it is critical to learn a desired dictionary, aiming both good representational power and discriminative performance. In this paper, we propose a new dictionary learning model for…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
Automatic lyrics to polyphonic audio alignment is a challenging task not only because the vocals are corrupted by background music, but also there is a lack of annotated polyphonic corpus for effective acoustic modeling. In this work, we…
We introduce a novel way to incorporate prior information into (semi-) supervised non-negative matrix factorization, which we call differentiable dictionary search. It enables general, highly flexible and principled modelling of mixtures…
To cater to the needs of (Zero Knowledge) proofs for (mathematical) proofs, we describe a method to transform formal sentences in 2x2-matrices over multivariate polynomials with integer coefficients, such that usual proof-steps like…
State-of-the-art speech-to-text models typically employ Transformer-based encoders that model token dependencies via self-attention mechanisms. However, the quadratic complexity of self-attention in both memory and computation imposes…
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…
A new ESPRIT-based algorithm is proposed to estimate the direction-of-arrival of an arbitrary degree polynomial-phase signal with a single acoustic vector sensor. The proposed approach requires neither a priori knowledge of the…
In this paper, we present a new method via the transfer matrix approach to obtain asymptotic formulae of orthogonal polynomials with asymptotically identical coefficients of bounded variation. We make use of the hyperbolicity of the…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…