no code implementations • 5 Feb 2024 • Lorenzo Masoero, Mario Beraha, Thomas Richardson, Stefano Favaro

In online randomized experiments or A/B tests, accurate predictions of participant inclusion rates are of paramount importance.

no code implementations • 26 Jan 2024 • Mario Beraha, Lorenzo Masoero, Stefano Favaro, Thomas S. Richardson

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.

no code implementations • 27 Sep 2023 • Mario Beraha, Stefano Favaro, Matteo Sesia

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.

no code implementations • 12 Jul 2023 • Stefano Favaro, Boris Hanin, Domenico Marinucci, Ivan Nourdin, Giovanni Peccati

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 $n$.

no code implementations • 8 Apr 2023 • Alberto Bordino, Stefano Favaro, Sandra Fortini

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.

no code implementations • 8 Apr 2023 • Alberto Bordino, Stefano Favaro, Sandra Fortini

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.

1 code implementation • 9 Nov 2022 • Matteo Sesia, Stefano Favaro, Edgar Dobriban

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.

no code implementations • 5 Sep 2022 • Stefano Favaro, Matteo Sesia

The estimation of coverage probabilities, and in particular of the missing mass, is a classical statistical problem with applications in numerous scientific fields.

no code implementations • 16 Jun 2022 • Stefano Favaro, Sandra Fortini, Stefano Peluchetti

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.

1 code implementation • 8 Apr 2022 • Matteo Sesia, Stefano Favaro

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.

no code implementations • 21 Mar 2022 • Emanuele Dolera, Stefano Favaro, Edoardo Mainini

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.

no code implementations • 20 Sep 2021 • Emanuele Dolera, Stefano Favaro

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.

no code implementations • 2 Aug 2021 • Stefano Favaro, Sandra Fortini, Stefano Peluchetti

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.

no code implementations • ICLR 2021 • Daniele Bracale, Stefano Favaro, Sandra Fortini, Stefano Peluchetti

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.

no code implementations • 8 Feb 2021 • Emanuele Dolera, Stefano Favaro, Stefano Peluchetti

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.

no code implementations • 7 Feb 2021 • Emanuele Dolera, Stefano Favaro, Stefano Peluchetti

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.

no code implementations • 7 Feb 2021 • Daniele Bracale, Stefano Favaro, Sandra Fortini, Stefano Peluchetti

The interplay between infinite-width neural networks (NNs) and classes of Gaussian processes (GPs) is well known since the seminal work of Neal (1996).

no code implementations • 7 Jul 2020 • Stefano Peluchetti, Stefano Favaro

Our results highlight a limited expressive power of doubly infinite ResNets when the unscaled network's parameters are i. i. d.

1 code implementation • 1 Mar 2020 • Stefano Favaro, Sandra Fortini, Stefano Peluchetti

We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions.

no code implementations • pproximateinference AABI Symposium 2019 • Lorenzo Masoero, Federico Camerlenghi, Stefano Favaro, Tamara Broderick

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.

1 code implementation • 11 Oct 2019 • Federico Camerlenghi, Bianca Dumitrascu, Federico Ferrari, Barbara E. Engelhardt, Stefano Favaro

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

no code implementations • 27 May 2019 • Stefano Peluchetti, Stefano Favaro

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.

no code implementations • 25 Jun 2018 • Fadhel Ayed, Marco Battiston, Federico Camerlenghi, Stefano Favaro

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?

no code implementations • 7 Jul 2016 • Marco Battiston, Stefano Favaro, Daniel M. Roy, Yee Whye Teh

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.

no code implementations • 16 Jul 2014 • María Lomelí, Stefano Favaro, Yee Whye Teh

We investigate the class of $\sigma$-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling.

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