## About

Some of the most significant advances in the recent history of statistics and data science have relied on our ability to express and exploit structure in data. This structure may be simple as in the case of parametric models such as linear regression, low rank matrix estimation or principal component analysis, where the data is assumed to be the superposition of a linear algebraic structure and some well behaved (e.g., Gaussian) noise. In other cases, this structure may be simple provided that the correct data representation is known, as is the case in wavelet thresholding for natural image denoising, where linearity arises in the wavelet basis space. The recent explosion of data that is routinely collected has led scientists to contemplate more and more sophisticated structural assumptions. In some cases such as models with latent variables, new models aim at capturing heterogeneity in the data, whereas in others, complex structures arise naturally as algebraic structures governed by the rigid laws of physics. Understanding how to harness and exploit such structure is key to improving the prediction accuracy of various learning procedures. The ultimate goal is to develop a set of tools that leverage underlying complex structures to pool information across observations and ultimately improve statistical accuracy as well as computational efficiency of the deployed methods. Bringing together computer scientists, mathematicians and statisticians will have a transformative impact in this fast developing avenue of research.

### Program

The workshop will take place at MIT (room 1-190) on January 27-29, 2020.

### Confirmed speakers

- Nima Anari (Stanford)
- Alex Dimakis (UT Austin)
- Aude Genevay (MIT)
- Tommi Jaakkola (MIT)
- Sham Kakade (U. of Washington)
- Tengyuan Liang (Booth School of Business)
- Tyler Maunu (MIT)
- Jonathan Niles-Weed (NYU/IAS)
- Ryan O'Donnell (CMU)
- Ioannis Panageas (SUTD)
- Miki Racz (Princeton)
- Andrej Risteski (CMU)
- Elina Robeva (U. of British Columbia)
- Sebastien Roch (U. of Wisconsin, Madison)
- Yaron Singer (Harvard)
- Justin Solomon (MIT)
- Vasilis Syrgkanis (Microsoft Research)
- Caroline Uhler (MIT/ETH Zurich)
- Gregory Valiant (Stanford)
- Cynthia Vizant (NC State)
- Alex Wein (NYU)
- Yihong Wu (Yale)

### Organizers

- Costis Daskalakis (MIT)
- Stefanie Jegelka (MIT)
- Jonathan Kelner (MIT)
- Ankur Moitra (MIT)
- Philippe Rigollet (MIT) -- Lead organizer

### Program

#### Day 1: Monday, January 27, 2020

Time | Speaker | Title |
---|---|---|

8:50 - 9:00 | Opening remarks | |

9:00 - 9:45 | Ioannis Panageas | Depth-width trade-offs for ReLU networks via Sharkovsky's theorem. |

9:45 - 10:30 | Ryan O'Donnell | Learning quantum states. |

10:30 - 11:00 | Coffee break | |

11:00 - 11:45 | Gregory Valiant | How bad is worst-case data if you understand where it comes from? |

11:45 - 12:30 | Yaron Singer | From predictions to decisions. |

12:30 - 2:00 | Lunch Break | |

2:00 - 2:45 | Miki Racz | Trace reconstruction problems with applications to DNA data storage |

2:45 - 3:30 | Sebastien Roch | Some statistical questions in evolutionary genomics. |

3:30 - 4:00 | Break | |

4:00 - 4:45 | Yihong Wu | Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in O(sqrt{n}) iterations. |

4:45 - 5:30 | Vasilis Syrgkanis | Statistical learning for causal inference. |

#### Day 2: Tuesday, January 28, 2020

Time | Speaker | Title |
---|---|---|

9:00 - 9:45 | Elina Robeva | Learning totally positive distributions. |

9:45 - 10:30 | Caroline Uhler | Causal inference through permutation-based algorithms. |

10:30 - 11:00 | Coffee Break | |

11:00 - 11:45 | Cynthia Vizant | Log-concave polynomials, matroids, and expanders. |

11:45 - 12:30 | Nima Anari | Limited correlations, fractional log-concavity, and fast mixing random walks. |

12:30 - 2:00 | Lunch Break | |

2:00 - 2:45 | Sham Kakade | The provable effectiveness of policy gradient methods in reinforcement learning. |

2:45 - 3:30 | Andrej Risteski | Fast convergence for Langevin diļ¬usion with matrix manifold structure. |

3:30 - 4:00 | Break | |

4:00 - 6:00 | Reception and Poster Session in 2-290 |

#### Posters

Author | Title |
---|---|

Rajat Talak | A Theory of Uncertainty Variables for Learning Complex Structures |

Kaizheng Wang | An $\ell_p$ analysis of eigenvectors with applications to spectral clustering |

Yoni Shtiebel | Computational Linguistics |

Anirudh Sridhar | Correlated Randomly Growing Graphs |

Igor Gilitschenski | Deep Orientation Uncertainty Learning based on a Bingham Loss |

Aleksandrina Goeva | Discovering Spatially Coherent Gene Expression Patterns |

Niloy Biswas | Estimating Convergence of Markov Chains with Couplings |

Lorenzo Masoero | Predicting and maximizing the number of new genomic variants in a future experiment |

Feng Liu | Hierarchical Graphical Structure Learning for EEG Source Imaging |

Marwa El Halabi | Minimizing approximately submodular functions |

Jean-Baptiste Seby | Multi-Trek Separation in Linear Structural Equation Models |

Qiuyi Wu | Music Mining In Topic Modeling Approach For Improvisational Learning |

Maryam Aliakbarpour | New directions in testing properties of distributions |

Sai Ganesh Nagarajan | On the Analysis of EM for truncated mixtures of two Gaussians |

Alireza Fallah | On Theory of Model-Agnostic Meta-Learning Algorithms |

Nir Rosenfeld | Predicting Choice with Set-Dependent Aggregation |

Julia Gaudio | Sparse High-Dimensional Isotonic Regression |

Eren Can Kizildag | Stationary Points of Shallow Neural Networks with Quadratic Activation Function |

Raj Agrawal | The Kernel Interaction Trick: Fast Bayesian Discovery of Pairwise Interactions in High Dimensions |

Eshaan Nichani | Understanding Alignment and the Role of Depth in Linear Neural Networks |

Miri Adler | Understanding variations in single-cell data using evolutionary tradeoff theory |

#### Workshop, Day 3: Wednesday, January 29

Time | Speaker | Title |
---|---|---|

9:00 - 9:45 | Tengyuan Liang | On restricted lower isometry of kernels, risk of minimum-norm interpolants, and multiple descent phenomenon. |

9:45 - 10:30 | Alex Wein | Understanding statistical-vs-computational tradeoffs via the low-degree likelihood ratio. |

10:30 - 11:00 | Coffee Break | |

11:00 - 11:45 | Alex Dimakis | Deep generative models and inverse problems. |

11:45 - 12:30 | Tommi Jaakkola | Learning to represent and generate molecular graphs. |

12:30 - 2:00 | Lunch Break | |

2:00 - 2:45 | Jonathan Niles-Weed | Estimation of the Wasserstein distance in the spiked transport model. |

2:45 - 3:30 | Aude Genevay | Learning with Sinkhorn divergences: from optimal transport to MMD. |

3:30 - 4:00 | Break | |

4:00 - 4:45 | Justin Solomon | Approximating and manipulating probability distributions with optimal transport. |

4:45 - 5:30 | Tyler Maunu | Gradient descent algorithms for Bures-Wasserstein barycenters. |