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We use time- and frequency-domain techniques to quantify the extent to which long-distance interconnection of wind plants in the United States would reduce the variability of wind power output. Previous work has shown that interconnection of just a few wind plants across moderate distances could greatly reduce the ratio of fast- to slow-ramping generators in the balancing portfolio. We find that interconnection of aggregate regional wind plants would not reduce this ratio further but would reduce variability at all frequencies examined. Further, interconnection of just a few wind plants reduces the average hourly change in power output, but interconnection across regions provides little further reduction. Interconnection also reduces the magnitude of low-probability step changes and doubles firm power output (capacity available at least 92% of the time) compared with a single region. First-order analysis indicates that balancing wind and providing firm power with local natural gas turbines would be more cost-effective than with transmission interconnection. For net load, increased wind capacity would require more balancing resources but in the same proportions by frequency as currently, justifying the practice of treating wind as negative load.

Pumped hydropower storage can smooth output from intermittent renewable electricity generators and facilitate their large-scale use in energy systems. Germany has aggressive plans for wind power expansion, and pumped storage ramps quickly enough to smooth wind power and could profit from arbitrage on the short-term price fluctuations wind power strengthens. We consider five capacity alternatives for a pumped storage facility in Norway that practices arbitrage in the German spot market. Price forecasts given increased wind capacity are used to calculate profit-maximizing production schedules and annual revenue streams. Real options theory is used to value the investment opportunity, since unlike net present value, it accounts for uncertainty and intertemporal choice. Results show that the optimal investment strategy under the base scenario is to invest in the largest available plant approximately eight years into the option lifetime.

Climate change mitigation will require extensive decarbonization of the electricity sector. This thesis addresses both large-scale wind integration (Papers 1–3) and development of new energy technologies (Paper 4) in service of this goal. Compressed air energy storage (CAES) could be paired with a wind farm to provide firm, dispatchable baseload power, or serve as a peaking plant and capture upswings in electricity prices. Paper 1 presents a firm-level engineering-economic analysis of a wind/CAES system with a wind farm in central Texas, load in either Dallas or Houston, and a CAES plant whose location is profit-optimized. Of a range of market scenarios considered, the CAES plant is found to be profitable only given the existence of large and infrequent price spikes. Social benefits of wind/CAES include avoided construction of new generation capacity, improved air quality during peak demand, and increased economic surplus, but may not outweigh the private cost of the CAES system nor justify a subsidy. Like CAES, pumped hydropower storage (PHS) ramps quickly enough to smooth wind power and could profit from arbitrage on short-term price fluctuations exacerbated by large-scale wind. Germany has aggressive plans for wind power expansion, and Paper 2 analyzes an investment opportunity in a PHS facility in Norway that practices arbitrage in the German spot market. Price forecasts given increased wind capacity are used to calculate profit-maximizing production schedules and annual revenue streams. Real options theory is used to value the investment opportunity, since unlike net present value, it accounts for uncertainty and intertemporal choice. Results show that the optimal investment strategy under the base scenario is to wait approximately eight years then invest in the largest available plant. Paper 3 examines long-distance interconnection as an alternate method of wind power smoothing. Frequency-domain analysis indicates that interconnection of aggregate regional wind plants across much of the western and mid-western U.S. would not result in significantly greater smoothing than interconnection within a single region. Time-domain analysis shows that interconnection across regions reduces the magnitude of low-probability step changes and doubles firm power output (capacity available at least 92 % of the time) compared with a single region. An approximate cost analysis indicates that despite these benefits, balancing wind and providing firm power with local natural gas turbines would be more cost-effective than with transmission interconnection. Papers 1 and 3 demonstrate the need for further RD&D (research, development, and deployment) of low-carbon energy technologies. Energy technology development is highly uncertain but most often modeled as deterministic, which neglects the ability both to adapt RD&D strategy to changing conditions and to invest in initially high-cost technologies with small breakthrough probabilities. Paper 4 develops an analytical stochastic dynamic programming framework in which RD&D spending decreases the expected value of the stochastic cost of a technology. Results for a two-factor cost model (which separates RD&D into R&D and learning-by-doing) applied to carbon capture and sequestration (CCS) indicate that given 15 years until large-scale deployment, investment in the RD&D program is optimal over a very broad range of initial mitigation costs ( $10–$ 380/tCO2). While the NPV of the program is zero if initial mitigation cost is$100/tCO2, under uncertainty the program is worth about $ 7 billion. If initial mitigation cost is high, the program is worth most if cost reductions exogenous to the program (e.g. due to private sector activity) are also high. Factors that promote R&D spending over learning-by-doing include more imminent deployment, high initial cost, lower exogenous cost reductions, and lower program funds available.

Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose embedded-model flows (EMF), which alternate general-purpose transformations with structured layers that embed domain-specific inductive biases. These layers are automatically constructed by converting user-specified differentiable probabilistic models into equivalent bijective transformations. We also introduce gated structured layers, which allow bypassing the parts of the models that fail to capture the statistics of the data. We demonstrate that EMFs can be used to induce desirable properties such as multimodality, hierarchical coupling and continuity. Furthermore, we show that EMFs enable a high performance form of variational inference where the structure of the prior model is embedded in the variational architecture. In our experiments, we show that this approach outperforms state-of-the-art methods in common structured inference problems.

Google Vizier has performed millions of optimizations and accelerated numerous research and production systems at Google, demonstrating the success of Bayesian optimization as a large-scale service. Over multiple years, its algorithm has been improved considerably, through the collective experiences of numerous research efforts and user feedback. In this technical report, we discuss the implementation details and design choices of the current default algorithm provided by Open Source Vizier. Our experiments on standardized benchmarks reveal its robustness and versatility against well-established industry baselines on multiple practical modes.

In this paper, we investigate the degree to which the encoding of a \\(\\beta\\)-VAE captures label information across multiple architectures on Binary Static MNIST and Omniglot. Even though they are trained in a completely unsupervised manner, we demonstrate that a \\(\\beta\\)-VAE can retain a large amount of label information, even when asked to learn a highly compressed representation.

Variational autoencoders learn unsupervised data representations, but these models frequently converge to minima that fail to preserve meaningful semantic information. For example, variational autoencoders with autoregressive decoders often collapse into autodecoders, where they learn to ignore the encoder input. In this work, we demonstrate that adding an auxiliary decoder to regularize the latent space can prevent this collapse, but successful auxiliary decoding tasks are domain dependent. Auxiliary decoders can increase the amount of semantic information encoded in the latent space and visible in the reconstructions. The semantic information in the variational autoencoder's representation is only weakly correlated with its rate, distortion, or evidence lower bound. Compared to other popular strategies that modify the training objective, our regularization of the latent space generally increased the semantic information content.

Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family. Here, we introduce automatic structured variational inference (ASVI), a fully automated method for constructing structured variational families, inspired by the closed-form update in conjugate Bayesian models. These convex-update families incorporate the forward pass of the input probabilistic program and can therefore capture complex statistical dependencies. Convex-update families have the same space and time complexity as the input probabilistic program and are therefore tractable for a very large family of models including both continuous and discrete variables. We validate our automatic variational method on a wide range of low- and high-dimensional inference problems. We find that ASVI provides a clear improvement in performance when compared with other popular approaches such as the mean-field approach and inverse autoregressive flows. We provide an open source implementation of ASVI in TensorFlow Probability.

Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive uncertainty. Quantifying uncertainty is especially critical in real-world settings, which often involve input distributions that are shifted from the training distribution due to a variety of factors including sample bias and non-stationarity. In such settings, well calibrated uncertainty estimates convey information about when a model's output should (or should not) be trusted. Many probabilistic deep learning methods, including Bayesian-and non-Bayesian methods, have been proposed in the literature for quantifying predictive uncertainty, but to our knowledge there has not previously been a rigorous large-scale empirical comparison of these methods under dataset shift. We present a large-scale benchmark of existing state-of-the-art methods on classification problems and investigate the effect of dataset shift on accuracy and calibration. We find that traditional post-hoc calibration does indeed fall short, as do several other previous methods. However, some methods that marginalize over models give surprisingly strong results across a broad spectrum of tasks.

Discriminative neural networks offer little or no performance guarantees when deployed on data not generated by the same process as the training distribution. On such out-of-distribution (OOD) inputs, the prediction may not only be erroneous, but confidently so, limiting the safe deployment of classifiers in real-world applications. One such challenging application is bacteria identification based on genomic sequences, which holds the promise of early detection of diseases, but requires a model that can output low confidence predictions on OOD genomic sequences from new bacteria that were not present in the training data. We introduce a genomics dataset for OOD detection that allows other researchers to benchmark progress on this important problem. We investigate deep generative model based approaches for OOD detection and observe that the likelihood score is heavily affected by population level background statistics. We propose a likelihood ratio method for deep generative models which effectively corrects for these confounding background statistics. We benchmark the OOD detection performance of the proposed method against existing approaches on the genomics dataset and show that our method achieves state-of-the-art performance. We demonstrate the generality of the proposed method by showing that it significantly improves OOD detection when applied to deep generative models of images.