相关论文: Approximate $\mathbb{F}_2$-Sketching of Valuation …

One of the arguments to explain the success of deep learning is the powerful approximation capacity of deep neural networks. Such capacity is generally accompanied by the explosive growth of the number of parameters, which, in turn, leads…

Streaming computation plays an important role in large-scale data analysis. The sliding window model is a model of streaming computation which also captures the recency of the data. In this model, data arrives one item at a time, but only…

Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality…

Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…

We introduce average-distortion sketching for metric spaces. As in (worst-case) sketching, these algorithms compress points in a metric space while approximately recovering pairwise distances. The novelty is studying average-distortion: for…

Preventing catastrophic forgetting while continually learning new tasks is an essential problem in lifelong learning. Structural regularization (SR) refers to a family of algorithms that mitigate catastrophic forgetting by penalizing the…

Maximizing submodular functions have been studied extensively for a wide range of subset-selection problems. However, much less attention has been given to the role of submodularity in sequence-selection and ranking problems. A…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…

Approximating quantiles and distributions over streaming data has been studied for roughly two decades now. Recently, Karnin, Lang, and Liberty proposed the first asymptotically optimal algorithm for doing so. This manuscript complements…

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as…

Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest…

We give near-optimal algorithms for computing an ellipsoidal rounding of a convex polytope whose vertices are given in a stream. The approximation factor is linear in the dimension (as in John's theorem) and only loses an excess logarithmic…

Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation…

We present a new approach for computing compact sketches that can be used to approximate the inner product between pairs of high-dimensional vectors. Based on the Weighted MinHash algorithm, our approach admits strong accuracy guarantees…

Network embeddings have become very popular in learning effective feature representations of networks. Motivated by the recent successes of embeddings in natural language processing, researchers have tried to find network embeddings in…

We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…

We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…

Recently, considerable research attention has been paid to network embedding, a popular approach to construct feature vectors of vertices. Due to the curse of dimensionality and sparsity in graphical datasets, this approach has become…

Leveraging the kernel trick in both the input and output spaces, surrogate kernel methods are a flexible and theoretically grounded solution to structured output prediction. If they provide state-of-the-art performance on complex data sets…