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Recent advances in computing hardware (FPGAs, distributed parallel computing) and numerical methods (machine learning algorithms, automatic differentiation) create new possibilities for Fusion Power Plant optimization and control. In this talk, I will discuss some of the recent accomplishments of the Plasma Control Group at Princeton that take advantage of these new capabilities.
How did scientists make sense of data before statistics and computing? This talk will explore this question by focusing on the discovery of vitamins, which occurred in the early 20th century just before the advent of modern statistical methodology. I will describe the varied practices in experimentation and reporting and highlight the sorts of insights required to uncover what "works." Through this discussion, I will draw connections to contemporary data science tools to illustrate their pros and cons in facilitating discovery.
The European Human Brain Project, a flagship project of the European Union, recently ended after 10 years of research and development. The goals of the HBP were to (1) explore the complexity of the human brain in space and time; (2) to transfer the knowledge broadly; (3) to provide research infrastructure for neuro-science; and (4) to create a community of researchers. One of the major challenges is to model neural activity, from micro- to macro-scale, in a way that enables simulation of the human brain. This leads to so-called in silico experiments, which will be used “to validate models, and to perform investigations that are not possible in the laboratory”. I will present examples of such experiments and discuss how they relate to, and can benefit from, statistical research on the design and analysis of computer experiments. My students and colleagues and I have been working on the potential advantages of replacing a slow/expensive simulator with a much faster and cheaper statistical emulator. Emulators are empirical replicas trained on data generated with the simulator. We have often used Gaussian process regression for this purpose, but in some applications other methods (random forests, polynomial regression) proved more effective. Emulators can be especially useful when the simulator runs are matched to data in the context of statistical inference. I will discuss the modeling options and present examples, including simulation of neural basket cells, calcium induced neural reactions, and stochastic simulators like the Hodgkin-Huxley model.
Machine learning and high-dimensional inference are a wellspring of fundamental algorithmic challenges in data science. In this talk, I will discuss two strands of work in this line of research. (i) In the first part, I will talk about ""estimation of fit"" type problems -- the high level goal here is to understand how well the best model (from a class of models) fits the target data. My focus will be on ""sparse models"", a standard assumption in machine learning to deal with data deficiency. In this setting, we design algorithms for estimating fit where the complexity scales just in the sparsity parameter and is independent of the ambient dimension. (ii) In the second part, I will discuss ""noisy reconstruction problems"" where the algorithm gets access to the target object through noisy samples. This formulation captures many well studied problems in machine learning. We give a new general algorithmic technique for such problems based on Fourier analysis which we refer to as "Fourier stability" and use this to design new, state of the art algorithms for "population recovery" and "trace reconstruction" -- two basic problems in unsupervised learning which have received significant attention in theoretical computer science. Our algorithms leverage methods and techniques from Boolean function analysis -- a set of tools at the intersection of analysis and combinatorics -- which has been very influential in complexity theory, especially in areas like PCPs and hardness of approximation. Synergistically, the development of this new algorithmic toolkit for problems in learning and inference has also led to discovery of results of intrinsic interest to probability theory and analysis, some of which I will briefly survey.
Abstract: Domain adaptation, transfer, multitask, meta, few-shots, or lifelong learning … these are all important recent directions in ML that all touch at the core of what we might mean by ‘AI’. As these directions all concern learning in heterogeneous and ever-changing environments, they all share a central question: what information a 'source' distribution may have […]
Data Science Day is held in collaboration with UCSD’s Halicioglu Data Science Institute and Rady School of Management. Tech San Diego works to highlight data science in the region by allowing local tech companies to talk about how they are using data science in their day-to-day operations. The day is broken into a panel discussion with three local organizations and a moderator followed by shorter “lightning talks” provided by faculty from the two collaborative institutions. The second half of the day is an event geared towards connecting emerging graduates and students with their professional counterparts to provide them an opportunity to network and ask real questions. We are so excited to return to the in-person format and look forward to see you all on campus again!
Differential privacy (DP) is widely regarded as a gold standard for privacy-preserving computation over users’ data. A key challenge with DP is that its mathematical sophistication makes its privacy guarantees difficult to communicate to users, leaving them uncertain about how and whether they are protected. Despite recent widespread deployment of DP, relatively little is known about what users think of differential privacy and how to effectively communicate the practical privacy guarantees it offers.
This talk will cover a series of recent and ongoing user studies aimed at measuring and improving communication with non-technical end users about differential privacy. The first set explores users' privacy expectations related to differential privacy and measures the efficacy of existing methods for communicating the privacy guarantees of DP systems. We find that users care about the kinds of information leaks against which differential privacy protects and are more willing to share their private information when the risk of these leaks is reduced. Additionally, we find that the ways in which differential privacy is described in-the-wild set users' privacy expectations haphazardly, which can be misleading depending on the deployment. Motivated by these findings, the second set of user studies develops and evaluates prototype descriptions designed to help end users understand DP guarantees. These descriptions target two important technical details in DP deployments that are often poorly communicated to end users: the privacy parameter epsilon (which governs the level of privacy protections) and the distinctions between the local and central models of DP (which governs who can access exact user data). Based on joint works with Gabriel Kaptchuk, Priyanka Nanayakkara, Elissa Redmiles, Mary Anne Smart, including https://arxiv.org/abs/2110.06452 and https://arxiv.org/abs/2303.00738.
A fundamental task in data analysis is to detect and recover a low-rank signal in a noisy data matrix. Typically, this task is addressed by inspecting and manipulating the spectrum of the observed data, e.g., thresholding the singular values of the data matrix at a certain critical level. This approach is well-established in the case of homoskedastic noise, where the noise variance is identical across the entries. However, in numerous applications, such as single-cell RNA sequencing (scRNA-seq), the noise can be heteroskedastic, where the noise characteristics vary considerably across the rows and columns of the data. In such scenarios, the noise spectrum can differ significantly from the homoskedastic case, posing various challenges for signal detection and recovery. In this talk, I will present a procedure for standardizing the noise spectrum by judiciously scaling the rows and columns of the data. Importantly, this procedure can provably enforce the standard spectral behavior of homoskedastic noise -- the Marchenko-Pastur law. I will describe methods for estimating the required scaling factors directly from the observed data with suitable theoretical justification, and demonstrate the advantages of the proposed approach for signal detection and recovery in simulations and on real scRNA-seq data.
Abstract: Recent advances in machine learning and artificial intelligence have relied on fitting highly overparameterized models, notably deep neural networks, to observed data. In such settings, the number of parameters of the model is much greater than the number of data samples, thereby resulting in a continuum of models with near-zero training error. Understanding which of these models generalize well and which do not is the central open question in deep learning. Recent empirical evidence suggests one mechanism for generalization: the shape of the training loss around a local minimizer seems to strongly impact the model’s performance. In particular, flat minima -- those around which the loss grows slowly -- appear to generalize well. Clarifying this phenomenon can shed new light on generalization in deep learning, which still largely remains a mystery.
I will describe our recent work that takes a step towards this goal by focusing on the simplest class of overparameterized nonlinear models: those arising in low-rank matrix recovery. We analyze overparameterized matrix and bilinear sensing, robust PCA, covariance matrix estimation, and single hidden layer neural networks with quadratic activation functions. In all cases, we show that flat minima, measured by the trace of the Hessian, exactly recover the ground truth under standard statistical assumptions. These results suggest (i) a theoretical basis for favoring methods that bias iterates towards flat solutions and (ii) use of Hessian trace as a good regularizer for some learning tasks. We end by discussing the impact of depth on the generalization properties of flat solutions, which surprisingly is not always beneficial.
Abstract: Causal inference has gained popularity due to its ability to draw causal conclusions for real-world questions. While much of the existing work in causal inference revolves around determining average treatment effects under no interference and no unmeasured confounding assumptions, these approaches may not be suitable for answering causal questions in complex settings. In the talk, we focus on the following three topics, each accompanied by relevant applications.
First, we discuss causal inference under interference and non-i.i.d. settings. Interference refers to a phenomenon where one’s outcome is affected by others’ treatment status; for instance, one’s own risk of flu infection is affected by family members’ flu vaccination status. We explore two estimators, a point-estimator and a bound-estimator, that are developed to infer causal effects in the presence of interference.
Second, we explore causal inference under the presence of unmeasured confounders, variables that affect both treatment status and outcome. We demonstrate that ignoring the potential existence of unmeasured confounding can lead to incorrect causal conclusions using data on the Zika virus outbreak. Recently developed frameworks, including universal difference-in-differences and single proxy control, are discussed to address the challenges posed by unmeasured confounding.