MIT Open Access Articles
https://hdl.handle.net/1721.1/49433
2020-08-04T08:54:01Z
2020-08-04T08:54:01Z
Inference via low-dimensional couplings
Spantini, Alessio
Bigoni, Daniele
Marzouk, Youssef M
https://hdl.handle.net/1721.1/126468
2020-08-04T03:00:45Z
2018-07-01T00:00:00Z
Inference via low-dimensional couplings
Spantini, Alessio; Bigoni, Daniele; Marzouk, Youssef M
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable “reference” measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map—e.g., representing and evaluating it—grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization—to the non-Gaussian case—of the square-root Rauch–Tung–Striebel Gaussian smoother.
2018-07-01T00:00:00Z
Exploiting network topology for large-scale inference of nonlinear reaction models
Galagali, Nikhil
Marzouk, Youssef M
https://hdl.handle.net/1721.1/126467
2020-08-04T03:21:10Z
2019-02-01T00:00:00Z
Exploiting network topology for large-scale inference of nonlinear reaction models
Galagali, Nikhil; Marzouk, Youssef M
The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to estimate unknown parameters but also to learn model structure. Bayesian inference provides a natural approach to this data-driven construction of models. Yet traditional Bayesian model inference methodologies that numerically evaluate the evidence for each model are often infeasible for nonlinear reaction network inference, as the number of plausible models can be combinatorially large. Alternative approaches based on model-space sampling can enable large-scale network inference, but their realization presents many challenges. In this paper, we present new computational methods that make large-scale nonlinear network inference tractable. First, we exploit the topology of networks describing potential interactions among chemical species to design improved 'between-model' proposals for reversible-jump Markov chain Monte Carlo. Second, we introduce a sensitivity-based determination of move types which, when combined with network-aware proposals, yields significant additional gains in sampling performance. These algorithms are demonstrated on inference problems drawn from systems biology, with nonlinear differential equation models of species interactions.
2019-02-01T00:00:00Z
On the complexity of energy storage problems
Halman, Nir
Nannicini, Giacomo
Orlin, James B
https://hdl.handle.net/1721.1/126466
2020-08-01T04:22:20Z
2017-12-01T00:00:00Z
On the complexity of energy storage problems
Halman, Nir; Nannicini, Giacomo; Orlin, James B
We analyze the computational complexity of the problem of optimally managing a storage device connected to a source of renewable energy, the power grid, and a household (or some other form of energy demand) in the presence of uncertainty. We provide a mathematical formulation for the problem as a Markov decision process following other models appearing in the literature, and study the complexity of determining a policy to achieve the maximum profit that can be attained over a finite time horizon, or simply the value of such profit. We show that if the problem is deterministic, i.e. there is no uncertainty on prices, energy production, or demand, the problem can be solved in strongly polynomial time. This is also the case in the stochastic setting if energy can be sold and bought for the same price on the spot market. If the sale and buying price are allowed to be different, the stochastic version of the problem is #P-hard, even if we are only interested in determining whether there exists a policy that achieves positive profit. Furthermore, no constant-factor approximation algorithm is possible in general unless P = NP. However, we provide a Fully Polynomial-Time Approximation Scheme (FPTAS) for the variant of the problem in which energy can only be bought from the grid, which is #P-hard. ©2017 Elsevier B.V.
2017-12-01T00:00:00Z
High repetition-rate femtosecond stimulated Raman spectroscopy with fast acquisition
Ashner, Matthew N.(Matthew Nickol)
Tisdale, William
https://hdl.handle.net/1721.1/126465
2020-08-01T03:26:56Z
2018-07-01T00:00:00Z
High repetition-rate femtosecond stimulated Raman spectroscopy with fast acquisition
Ashner, Matthew N.(Matthew Nickol); Tisdale, William
Time-resolved femtosecond stimulated Raman spectroscopy (FSRS) is a powerful tool for investigating ultrafast structural and vibrational dynamics in light absorbing systems. However, the technique generally requires exposing a sample to high laser pulse fluences and long acquisition times to achieve adequate signal-to-noise ratios. Here, we describe a time-resolved FSRS instrument built around a Yb ultrafast amplifier operating at 200 kHz, and address some of the unique challenges that arise at high repetition-rates. The setup includes detection with a 9 kHz CMOS camera and an improved dual-chopping scheme to reject scattering artifacts that occur in the 3-pulse configuration. The instrument demonstrates good signal-to-noise performance while simultaneously achieving a 3-6 fold reduction in pulse energy and a 5-10 fold reduction in acquisition time relative to comparable 1 kHz instruments. ©2018 Optical Society of America.
2018-07-01T00:00:00Z