IPAM Workshop on Algorithmic Challenges in Protecting Privacy for Biomedical Data

IPAM is hosting a workshop on Algorithmic Challenges in Protecting Privacy for Biomedical Data” which will be held at IPAM from January 10-12, 2018.

The workshop will be attended by many junior as well as senior researchers with diverse backgrounds. We want to to encourage students or postdoctoral scholars who might be interested, to apply and/or register for this workshop.

I think it will be quite interesting and has the potential to spark a lot of interesting conversations around what we can and cannot do about privacy for medical data in general and genomic data in specific.

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DIMACS Workshop on Distributed Optimization, Information Processing, and Learning

My colleague Waheed Bajwa, Alejandro Ribeiro, and Alekh Agarwal are organizing a Workshop on Distributed Optimization, Information Processing, and Learning from August 21 to August 23, 2017 at Rutgers DIMACS. The purpose of this workshop is to bring together researchers from the fields of machine learning, signal processing, and optimization for cross-pollination of ideas related to the problems of distributed optimization, information processing, and learning. All in all, we are expecting to have 20 to 26 invited talks from leading researchers working in these areas as well as around 20 contributed posters in the workshop.

Registration is open from now until August 14 — hope to see some of you there!

Mathematical Tools of Information-Theoretic Security Workshop: Day 1

It’s been a while since I have conference-blogged but I wanted to set aside a little time for it. Before going to Allerton I went to a lovely workshop in Paris on the Mathematical Tools of Information-Theoretic Security thanks to a very kind invitation from Vincent Tan and Matthieu Bloch. This was a 2.5 day workshop covering a rather wide variety of topics, which was good for me since I learned quite a bit. I gave a talk on differential privacy and machine learning with a little more of a push on the mathematical aspects that might be interesting from an information-theory perspective. Paris was appropriately lovely, and it was great to see familiar and new faces there. Now that I am at Rutgers I should note especially our three distinguished alumnae, Şennur Ulukuş, Aylin Yener, and Lalitha Sankar.

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ISIT 2015 : statistics and learning

The advantage of flying to Hong Kong from the US is that the jet lag was such that I was actually more or less awake in the mornings. I didn’t take such great notes during the plenaries, but they were rather enjoyable, and I hope that the video will be uploaded to the ITSOC website soon.

There were several talks on entropy estimation in various settings that I did not take great notes on, to wit:

  • OPTIMAL ENTROPY ESTIMATION ON LARGE ALPHABETS VIA BEST POLYNOMIAL APPROXIMATION (Yihong Wu, Pengkun Yang, University Of Illinois, United States)
  • DOES DIRICHLET PRIOR SMOOTHING SOLVE THE SHANNON ENTROPY ESTIMATION PROBLEM? (Yanjun Han, Tsinghua University, China; Jiantao Jiao, Tsachy Weissman, Stanford University, United States)
  • ADAPTIVE ESTIMATION OF SHANNON ENTROPY (Yanjun Han, Tsinghua University, China; Jiantao Jiao, Tsachy Weissman, Stanford University, United States)

I would highly recommend taking a look for those who are interested in this problem. In particular, it looks like we’re getting towards more efficient entropy estimators in difficult settings (online, large alphabet), which is pretty exciting.

QUICKEST LINEAR SEARCH OVER CORRELATED SEQUENCES
Javad Heydari, Ali Tajer, Rensselaer Polytechnic Institute, United States
This talk was about hypothesis testing where the observer can control the samples being taken by traversing a graph. We have an n-node graph (c.f. a graphical model) representing the joint distribution on n variables. The data generated is i.i.d. across time according to either F_0 or F_1. At each time you get to observe the data from only one node of the graph. You can either observe the same node as before, explore by observing a different node, or make a decision about whether the data from from F_0 or F_1. By adopting some costs for different actions you can form a dynamic programming solution for the search strategy but it’s pretty heavy computationally. It turns out the optimal rule for switching has a two-threshold structure and can be quite a bit different than independent observations when the correlations are structured appropriately.

MISMATCHED ESTIMATION IN LARGE LINEAR SYSTEMS
Yanting Ma, Dror Baron, North Carolina State University, United States; Ahmad Beirami, Duke University, United States
The mismatch studied in this paper is a mismatch in the prior distribution for a sparse observation problem y = Ax + \sigma_z z, where x \sim P (say a Bernoulli-Gaussian prior). The question is what happens when we do estimation assuming a different prior Q. The main result of the paper is an analysis of the excess MSE using a decoupling principle. Since I don’t really know anything about the replica method (except the name “replica method”), I had a little bit of a hard time following the talk as a non-expert, but thankfully there were a number of pictures and examples to help me follow along.

SEARCHING FOR MULTIPLE TARGETS WITH MEASUREMENT DEPENDENT NOISE
Yonatan Kaspi, University of California, San Diego, United States; Ofer Shayevitz, Tel-Aviv University, Israel; Tara Javidi, University of California, San Diego, United States
This was another search paper, but this time we have, say, K targets W_1, W_2, \ldots, W_K uniformly distributed in the unit interval, and what we can do is query at each time n a set S_n \subseteq [0,1] and get a response Y_n = X_n \oplus Z_n where X_n = \mathbf{1}( \exists W_k \in S_n ) and Z_n \sim \mathrm{Bern}( \mu(S_n) + b ) where \mu is the Lebesgue measure. So basically you can query a set and you get a noisy indicator of whether you hit any targets, where the noise depends on the size of the set you query. At some point \tau you stop and guess the target locations. You are (\epsilon,\delta) successful if the probability that you are within \delta of each target is less than \epsilon. The targeting rate is the limit of \log(1/\delta) / \mathbb{E}[\tau] as \epsilon,\delta \to 0 (I’m being fast and loose here). Clearly there are some connections to group testing and communication with feedback, etc. They show there is a significant gap between the adaptive and nonadaptive rate here, so you can find more targets if you can adapt your queries on the fly. However, since rate is defined for a fixed number of targets, we could ask how the gap varies with K. They show it shrinks.

ON MODEL MISSPECIFICATION AND KL SEPARATION FOR GAUSSIAN GRAPHICAL MODELS
Varun Jog, University of California, Berkeley, United States; Po-Ling Loh, University of Pennsylvania, United States
The graphical model for jointly Gaussian variables has no edge between nodes i and j if the corresponding entry (\Sigma^{-1})_{ij} = 0 in the inverse covariance matrix. They show a relationship between the KL divergence of two distributions and their corresponding graphs. The divergence is lower bounded by a constant if they differ in a single edge — this indicates that estimating the edge structure is important when estimating the distribution.

CONVERSES FOR DISTRIBUTED ESTIMATION VIA STRONG DATA PROCESSING INEQUALITIES
Aolin Xu, Maxim Raginsky, University of Illinois at Urbana–Champaign, United States
Max gave a nice talk on the problem of minimizing an expected loss \mathbb{E}[ \ell(W, \hat{W}) ] of a d-dimensional parameter W which is observed noisily by separate encoders. Think of a CEO-style problem where there is a conditional distribution P_{X|W} such that the observation at each node is a d \times n matrix whose columns are i.i.d. and where the j-th row is i.i.d. according to P_{X|W_j}. Each sensor gets independent observations from the same model and can compress its observations to b bits and sends it over independent channels to an estimator (so no MAC here). The main result is a lower bound on the expected loss as s function of the number of bits latex b, the mutual information between W and the final estimate \hat{W}. The key is to use the strong data processing inequality to handle the mutual information — the constants that make up the ratio between the mutual informations is important. I’m sure Max will blog more about the result so I’ll leave a full explanation to him (see what I did there?)

More on Shannon theory etc. later!

AISTATS 2015: a few talks from one day

I attended AISTATS for about a day and change this year — unfortunately due to teaching I missed the poster I had there but Shuang Song presented a work on learning from data sources of different quality, which her work with Kamalika Chaudhuri and myself. This was my first AISTATS. It had single track of oral presentations and then poster sessions for the remaining papers. The difficulty with a single track for me is that my interest in the topics is relatively focused, and the format of a general audience with a specialist subject matter meant that I couldn’t get as much out of the talks as I would have wanted. Regardless, I did get exposed to a number of new problems. Maybe the ideas can percolate for a while and inform something in the future.

Computational Complexity of Linear Large Margin Classification With Ramp Loss
Søren Frejstrup Maibing, Christian Igel
The main result of this paper (I think) is that ERM under ramp loss is NP-hard. They gave the details of the reduction but since I’m not a complexity theorist I got a bit lost in the weeds here.

A la Carte — Learning Fast Kernels
Zichao Yang, Andrew Wilson, Alex Smola, Le Song
Ideas like “random kitchen sinks” and other kernel approximation methods require you to have a kernel you want to approximate, but in many problems you in fact need to learn the kernel from the data. If I give you a kernel function k(x,x') = k( |x - x'| ), then you can take the Fourier transform K(\omega) of k. This turns out to be a probability distribution, so you can sample random \{\omega_i\} i.i.d. and build a randomized Fourier approximation of k. If you don’t know the kernel function, or you have to learn it, then you could instead try to learn/estimate the transform directly. This paper was about trying to do that in a reasonably efficient way.

Learning Where to Sample in Structured Prediction
Tianlin Shi, Jacob Steinhardt, Percy Liang
This was about doing Gibbs sampling, not for MCMC sampling from the stationary distribution, but for “stochastic search” or optimization problems. The intuition was that some coordinates are “easier” than others, so we might want to focus resampling on the harder coordinates. But this might lead to inaccurate sampling. The aim here twas to build a heterogenous sampler that is cheap to compute and still does the right thing.

Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning
Mario Lucic, Mesrob Ohannessian, Amin Karbasi, Andreas Krause
This paper won the best student paper award. They looked at a k-means problem where they do “data summarization” to make the problem a bit more efficient — that is, by learning over an approximation/summary of the features, they can find different tradeoffs between the running time, risk, and sample size for learning problems. The idea is to use coresets — I’d recommend reading the paper to get a better sense of what is going on. It’s on my summer reading list.

Averaged Least-Mean-Squares: Bias-Variance Trade-offs and Optimal Sampling Distributions
Alexandre Defossez, Francis Bach
What if you want to do SGD but you don’t want to sample the points uniformly? You’ll get a bias-variance tradeoff. This is another one of those “you have to read the paper” presentations. A nice result if you know the background literature, but if you are not a stochastic gradient aficionado, you might be totally lost.

Sparsistency of \ell_1-Regularized M-Estimators
Yen-Huan Li, Jonathan Scarlett, Pradeep Ravikumar, Volkan Cevher
In this paper they find a new condition, which they call local structured smoothness, which is sufficient for certain M-estimators to be “sparsistent” — that is, they recover the support pattern of a sparse parameter asymptotically as the number of data points goes to infinity. Examples include the LASSO, regression in general linear models, and graphical model selection.

Some of the other talks which were interesting but for which my notes were insufficient:

  • Two-stage sampled learning theory on distributions (Zoltan Szabo, Arthur Gretton, Barnabas Poczos, Bharath Sriperumbudur)
  • Generalized Linear Models for Aggregated Data (Avradeep Bhowmik, Joydeep Ghosh, Oluwasanmi Koyejo)
  • Efficient Estimation of Mutual Information for Strongly Dependent Variables (Shuyang Gao, Greg Ver Steeg, Aram Galstyan)
  • Sparse Submodular Probabilistic PCA (Rajiv Khanna, Joydeep Ghosh, Russell Poldrack, Oluwasanmi Koyejo)

2015 North American School of Information Theory

The 2015 ​North American ​School of Information Theory ​(NASIT) will be held on August 10-13, 2015, at the University of California, San Diego in La Jolla. If you or your colleagues have students who might be interested in this event, we would be grateful if you could forward this email to them and encourage their participation. The application deadline is ​Sunday, June 7. As in the past schools, we again have a great set of lecturers this year​​:

We are pleased to announce that ​Paul Siegel will be the​​ Padovani Lecturer of the IEEE Information Theory Society​​ and will give his lecture at the School. The Padovani Lecture is sponsored by a generous gift of Roberto Padovani.

For more information and application, please visit the School website.​​

2015 Bellairs Workshop on Large-Scale Inference and Optimization

A few weeks ago I got to go to Bellairs in Holetown, Barbados for a workshop organized by Mike Rabbat and Mark Coates of McGill University. It’s a small workshop, mostly for Mike and Mark’s students, and it’s a chance to interact closely and perhaps start some new research collaborations. Here’s a brief summary of the workshop as I remember it from my notes.

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