Zobrazeno 1 - 10
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pro vyhledávání: '"Kannan, Ravindran"'
A central problem related to transformers can be stated as follows: given two $n \times d$ matrices $Q$ and $K$, and a non-negative function $f$, define the matrix $A$ as follows: (1) apply the function $f$ to each entry of the $n \times n$ matrix $Q
Externí odkaz:
http://arxiv.org/abs/2410.05462
The Separating Hyperplane theorem is a fundamental result in Convex Geometry with myriad applications. Our first result, Random Separating Hyperplane Theorem (RSH), is a strengthening of this for polytopes. $\rsh$ asserts that if the distance between
Externí odkaz:
http://arxiv.org/abs/2307.11371
$k-$means Clustering requires as input the exact value of $k$, the number of clusters. Two challenges are open: (i) Is there a data-determined definition of $k$ which is provably correct and (ii) Is there a polynomial time algorithm to find $k$ from
Externí odkaz:
http://arxiv.org/abs/2012.04388
In this paper we show that a large class of Latent variable models, such as Mixed Membership Stochastic Block(MMSB) Models, Topic Models, and Adversarial Clustering, can be unified through a geometric perspective, replacing model specific assumptions
Externí odkaz:
http://arxiv.org/abs/1904.06738
Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a str
Externí odkaz:
http://arxiv.org/abs/1410.6991
We study spectral algorithms for the high-dimensional Nearest Neighbor Search problem (NNS). In particular, we consider a semi-random setting where a dataset $P$ in $\mathbb{R}^d$ is chosen arbitrarily from an unknown subspace of low dimension $k\ll
Externí odkaz:
http://arxiv.org/abs/1408.0751
We consider algorithmic problems in the setting in which the input data has been partitioned arbitrarily on many servers. The goal is to compute a function of all the data, and the bottleneck is the communication used by the algorithm. We present alg
Externí odkaz:
http://arxiv.org/abs/1304.3162
Autor:
Kumar, Amit, Kannan, Ravindran
There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between the means
Externí odkaz:
http://arxiv.org/abs/1004.1823
Autor:
Kannan, Ravindran
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete optimizat
Externí odkaz:
http://arxiv.org/abs/1004.1253