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Found 25 papers, 4 papers with code
Improved prediction of future user activity in online A/B testing
In online randomized experiments or A/B tests, accurate predictions of participant inclusion rates are of paramount importance.
A Nonparametric Bayes Approach to Online Activity Prediction
We derive closed-form expressions for the number of new users expected in a given period, and a simple Monte Carlo algorithm targeting the posterior distribution of the number of days needed to attain a desired number of users; the latter is important for experimental planning.
Frequency and cardinality recovery from sketched data: a novel approach bridging Bayesian and frequentist views
We study how to recover the frequency of a symbol in a large discrete data set, using only a compressed representation, or sketch, of those data obtained via random hashing.
Quantitative CLTs in Deep Neural Networks
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$.
Non-asymptotic approximations of Gaussian neural networks via second-order Poincaré inequalities
There is a growing interest on large-width asymptotic properties of Gaussian neural networks (NNs), namely NNs whose weights are initialized according to Gaussian distributions.
Infinitely wide limits for deep Stable neural networks: sub-linear, linear and super-linear activation functions
As a novelty with respect to previous works, our results rely on the use of a generalized central limit theorem for heavy tails distributions, which allows for an interesting unified treatment of infinitely wide limits for deep Stable NNs.
Conformal Frequency Estimation using Discrete Sketched Data with Coverage for Distinct Queries
This paper develops conformal inference methods to construct a confidence interval for the frequency of a queried object in a very large discrete data set, based on a sketch with a lower memory footprint.
Bayesian nonparametric estimation of coverage probabilities and distinct counts from sketched data
The estimation of coverage probabilities, and in particular of the missing mass, is a classical statistical problem with applications in numerous scientific fields.
Large-width asymptotics for ReLU neural networks with $α$-Stable initializations
As a difference with respect to the Gaussian setting, our result shows that the choice of the activation function affects the scaling of the NN, that is: to achieve the infinitely wide $\alpha$-Stable process, the ReLU activation requires an additional logarithmic term in the scaling with respect to sub-linear activations.
Conformal Frequency Estimation with Sketched Data
A flexible conformal inference method is developed to construct confidence intervals for the frequencies of queried objects in very large data sets, based on a much smaller sketch of those data.
Strong posterior contraction rates via Wasserstein dynamics
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity.
The power of private likelihood-ratio tests for goodness-of-fit in frequency tables
This is obtained through a Bahadur-Rao large deviation expansion for the power of the private LR test, bringing out a critical quantity, as a function of the sample size, the dimension of the table and $(\varepsilon,\delta)$, that determines a loss in the power of the test.
Deep Stable neural networks: large-width asymptotics and convergence rates
Then, we establish sup-norm convergence rates of the rescaled deep Stable NN to the Stable SP, under the ``joint growth" and a ``sequential growth" of the width over the NN's layers.
Large-width functional asymptotics for deep Gaussian neural networks
In this paper, we consider fully connected feed-forward deep neural networks where weights and biases are independent and identically distributed according to Gaussian distributions.
Learning-augmented count-min sketches via Bayesian nonparametrics
Under this more general framework, we apply the arguments of the ``Bayesian" proof of the CMS-DP, suitably adapted to the PYP prior, in order to compute the posterior distribution of a point query, given the hashed data.
Infinite-channel deep stable convolutional neural networks
The interplay between infinite-width neural networks (NNs) and classes of Gaussian processes (GPs) is well known since the seminal work of Neal (1996).
A Bayesian nonparametric approach to count-min sketch under power-law data streams
The count-min sketch (CMS) is a randomized data structure that provides estimates of tokens' frequencies in a large data stream using a compressed representation of the data by random hashing.
Doubly infinite residual neural networks: a diffusion process approach
Our results highlight a limited expressive power of doubly infinite ResNets when the unscaled network's parameters are i. i. d.
Stable behaviour of infinitely wide deep neural networks
We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions.
Genomic variety prediction via Bayesian nonparametrics
We consider the case where scientists have already conducted a pilot study to reveal some variants in a genome and are contemplating a follow-up study.
Nonparametric Bayesian multi-armed bandits for single cell experiment design
The problem of maximizing cell type discovery under budget constraints is a fundamental challenge for the collection and analysis of single-cell RNA-sequencing (scRNA-seq) data.
Applications
Infinitely deep neural networks as diffusion processes
When the parameters are independently and identically distributed (initialized) neural networks exhibit undesirable properties that emerge as the number of layers increases, e. g. a vanishing dependency on the input and a concentration on restrictive families of functions including constant functions.
On consistent estimation of the missing mass
Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw?
A characterization of product-form exchangeable feature probability functions
We characterize the class of exchangeable feature allocations assigning probability $V_{n, k}\prod_{l=1}^{k}W_{m_{l}}U_{n-m_{l}}$ to a feature allocation of $n$ individuals, displaying $k$ features with counts $(m_{1},\ldots, m_{k})$ for these features.
A marginal sampler for $σ$-Stable Poisson-Kingman mixture models
We investigate the class of $\sigma$-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling.
