相关论文: Approximate Vanishing Ideal Computations at Scale
We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…
As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable…
We study the problem of inferring a sparse vector from random linear combinations of its components. We propose the Accelerated Orthogonal Least-Squares (AOLS) algorithm that improves performance of the well-known Orthogonal Least-Squares…
Variational Inference (VI) offers a method for approximating intractable likelihoods. In neural VI, inference of approximate posteriors is commonly done using an encoder. Alternatively, encoderless VI offers a framework for learning…
Identifying optimal values for a high-dimensional set of hyperparameters is a problem that has received growing attention given its importance to large-scale machine learning applications such as neural architecture search. Recently…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
The concept of learning to optimize involves utilizing a trainable optimization strategy rather than relying on manually defined full gradient estimations such as ADAM. We present a framework that jointly trains the full gradient estimator…
Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. This study proposes gradient-only line searches to resolve the learning rate for…
Let $\K$ be a finite field and $X$ be a complete simplicial toric variety over $\K$. We give an algorithm relying on elimination theory for finding generators of the vanishing ideal of a subgroup $Y_Q$ parameterized by a matrix $Q$ which…
Uniform sampling and approximate counting are fundamental primitives for modern database applications, ranging from query optimization to approximate query processing. While recent breakthroughs have established optimal sampling and…
We consider an homogeneous ideal $I$ in the polynomial ring $S=K[x_1,\dots,$ $x_m]$ over a finite field $K=\mathbb{F}_q$ and the finite set of projective rational points $\mathbb{X}$ that it defines in the projective space…
The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several…
We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
The ellipsoid algorithm is a fundamental algorithm for computing a solution to the system of $m$ linear inequalities in $n$ variables $(P): A^{\top}x \le u$ when its set of solutions has positive volume. However, when $(P)$ is infeasible,…
We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for achieving quantum advantage in combinatorial optimization on Near-Term Intermediate-Scale Quantum (NISQ) devices. However, random initialization of the…
Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the…