We provide a unified framework for characterizing pure and approximate differentially private (DP) learnabiliity. The framework uses the language of graph theory: for a concept class $\mathcal{H}$, we define the contradiction graph $G$ of $\mathcal{H}$. It vertices are realizable datasets, and two datasets $S,S'$ are connected by an edge if they contradict each other (i.e., there is a point $x$ that is labeled differently in $S$ and $S'$). Our main finding is that the combinatorial structure of $G$ is deeply related to learning $\mathcal{H}$ under DP. Learning $\mathcal{H}$ under pure DP is captured by the fractional clique number of $G$. Learning $\mathcal{H}$ under approximate DP is captured by the clique number of $G$. Consequently, we identify graph-theoretic dimensions that characterize DP learnability: the clique dimension and fractional clique dimension. Along the way, we reveal properties of the contradiction graph which may be of independent interest. We also suggest several open questions and directions for future research.
In his seminal paper "Computing Machinery and Intelligence", Alan Turing introduced the "imitation game" as part of exploring the concept of machine intelligence. The Turing Test has since been the subject of much analysis, debate, refinement and extension. Here we sidestep the question of whether a particular machine can be labeled intelligent, or can be said to match human capabilities in a given context. Instead, but inspired by Turing, we draw attention to the seemingly simpler challenge of determining whether one is interacting with a human or with a machine, in the context of everyday life. We are interested in reflecting upon the importance of this Human-or-Machine question and the use one may make of a reliable answer thereto. Whereas Turing's original test is widely considered to be more of a thought experiment, the Human-or-Machine question as discussed here has obvious practical significance. And while the jury is still not in regarding the possibility of machines that can mimic human behavior with high fidelity in everyday contexts, we argue that near-term exploration of the issues raised here can contribute to development methods for computerized systems, and may also improve our understanding of human behavior in general.
Gibbard and Satterthwaite have shown that the only single-valued social choice functions (SCFs) that satisfy non-imposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by misrepresenting their preferences) are dictatorships. In this paper, we consider set-valued social choice correspondences (SCCs) that are strategyproof according to Fishburn's preference extension and, in particular, the top cycle, an attractive SCC that returns the maximal elements of the transitive closure of the weak majority relation. Our main theorem implies that, under mild conditions, the top cycle is the only non-imposing strategyproof SCC whose outcome only depends on the quantified pairwise comparisons between alternatives. This result effectively turns the Gibbard-Satterthwaite impossibility into a complete characterization of the top cycle by moving from SCFs to SCCs. It is obtained as a corollary of a more general characterization of strategyproof SCCs.
In decentralized settings, the shuffle model of differential privacy has emerged as a promising alternative to the classical local model. Analyzing privacy amplification via shuffling is a critical component in both single-message and multi-message shuffle protocols. However, current methods used in these two areas are distinct and specific, making them less convenient for protocol designers and practitioners. In this work, we introduce variation-ratio reduction as a unified framework for privacy amplification analyses in the shuffle model. This framework utilizes total variation bounds of local messages and probability ratio bounds of other users' blanket messages, converting them to indistinguishable levels. Our results indicate that the framework yields tighter bounds for both single-message and multi-message encoders (e.g., with local DP, local metric DP, or multi-message randomizers). Specifically, for a broad range of local randomizers having extremal probability design, our amplification bounds are precisely tight. We also demonstrate that variation-ratio reduction is well-suited for parallel composition in the shuffle model and results in stricter privacy accounting for common sampling-based local randomizers. Our experimental findings show that, compared to existing amplification bounds, our numerical amplification bounds can save up to $30\%$ of the budget for single-message protocols, $75\%$ of the budget for multi-message protocols, and $75\%$-$95\%$ of the budget for parallel composition. Additionally, our implementation for numerical amplification bounds has only $\tilde{O}(n)$ complexity and is highly efficient in practice, taking just $10$ seconds for $n=10^8$ users. The code for our implementation can be found at \url{//github.com/wangsw/PrivacyAmplification}.
Two numerical schemes are proposed and investigated for the Yang--Mills equations, which can be seen as a nonlinear generalisation of the Maxwell equations set on Lie algebra-valued functions, with similarities to certain formulations of General Relativity. Both schemes are built on the Discrete de Rham (DDR) method, and inherit from its main features: an arbitrary order of accuracy, and applicability to generic polyhedral meshes. They make use of the complex property of the DDR, together with a Lagrange-multiplier approach, to preserve, at the discrete level, a nonlinear constraint associated with the Yang--Mills equations. We also show that the schemes satisfy a discrete energy dissipation (the dissipation coming solely from the implicit time stepping). Issues around the practical implementations of the schemes are discussed; in particular, the assembly of the local contributions in a way that minimises the price we pay in dealing with nonlinear terms, in conjunction with the tensorisation coming from the Lie algebra. Numerical tests are provided using a manufactured solution, and show that both schemes display a convergence in $L^2$-norm of the potential and electrical fields in $\mathcal O(h^{k+1})$ (provided that the time step is of that order), where $k$ is the polynomial degree chosen for the DDR complex. We also numerically demonstrate the preservation of the constraint.
In federated frequency estimation (FFE), multiple clients work together to estimate the frequencies of their collective data by communicating with a server that respects the privacy constraints of Secure Summation (SecSum), a cryptographic multi-party computation protocol that ensures that the server can only access the sum of client-held vectors. For single-round FFE, it is known that count sketching is nearly information-theoretically optimal for achieving the fundamental accuracy-communication trade-offs [Chen et al., 2022]. However, we show that under the more practical multi-round FEE setting, simple adaptations of count sketching are strictly sub-optimal, and we propose a novel hybrid sketching algorithm that is provably more accurate. We also address the following fundamental question: how should a practitioner set the sketch size in a way that adapts to the hardness of the underlying problem? We propose a two-phase approach that allows for the use of a smaller sketch size for simpler problems (e.g. near-sparse or light-tailed distributions). We conclude our work by showing how differential privacy can be added to our algorithm and verifying its superior performance through extensive experiments conducted on large-scale datasets.
Computing an AUC as a performance measure to compare the quality of different machine learning models is one of the final steps of many research projects. Many of these methods are trained on privacy-sensitive data and there are several different approaches like $\epsilon$-differential privacy, federated machine learning and cryptography if the datasets cannot be shared or used jointly at one place for training and/or testing. In this setting, it can also be a problem to compute the global AUC, since the labels might also contain privacy-sensitive information. There have been approaches based on $\epsilon$-differential privacy to address this problem, but to the best of our knowledge, no exact privacy preserving solution has been introduced. In this paper, we propose an MPC-based solution, called ppAURORA, with private merging of individually sorted lists from multiple sources to compute the exact AUC as one could obtain on the pooled original test samples. With ppAURORA, the computation of the exact area under precision-recall and receiver operating characteristic curves is possible even when ties between prediction confidence values exist. We use ppAURORA to evaluate two different models predicting acute myeloid leukemia therapy response and heart disease, respectively. We also assess its scalability via synthetic data experiments. All these experiments show that we efficiently and privately compute the exact same AUC with both evaluation metrics as one can obtain on the pooled test samples in plaintext according to the semi-honest adversary setting.
Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.
Games and simulators can be a valuable platform to execute complex multi-agent, multiplayer, imperfect information scenarios with significant parallels to military applications: multiple participants manage resources and make decisions that command assets to secure specific areas of a map or neutralize opposing forces. These characteristics have attracted the artificial intelligence (AI) community by supporting development of algorithms with complex benchmarks and the capability to rapidly iterate over new ideas. The success of artificial intelligence algorithms in real-time strategy games such as StarCraft II have also attracted the attention of the military research community aiming to explore similar techniques in military counterpart scenarios. Aiming to bridge the connection between games and military applications, this work discusses past and current efforts on how games and simulators, together with the artificial intelligence algorithms, have been adapted to simulate certain aspects of military missions and how they might impact the future battlefield. This paper also investigates how advances in virtual reality and visual augmentation systems open new possibilities in human interfaces with gaming platforms and their military parallels.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
Deep learning methods for graphs achieve remarkable performance on many node-level and graph-level prediction tasks. However, despite the proliferation of the methods and their success, prevailing Graph Neural Networks (GNNs) neglect subgraphs, rendering subgraph prediction tasks challenging to tackle in many impactful applications. Further, subgraph prediction tasks present several unique challenges, because subgraphs can have non-trivial internal topology, but also carry a notion of position and external connectivity information relative to the underlying graph in which they exist. Here, we introduce SUB-GNN, a subgraph neural network to learn disentangled subgraph representations. In particular, we propose a novel subgraph routing mechanism that propagates neural messages between the subgraph's components and randomly sampled anchor patches from the underlying graph, yielding highly accurate subgraph representations. SUB-GNN specifies three channels, each designed to capture a distinct aspect of subgraph structure, and we provide empirical evidence that the channels encode their intended properties. We design a series of new synthetic and real-world subgraph datasets. Empirical results for subgraph classification on eight datasets show that SUB-GNN achieves considerable performance gains, outperforming strong baseline methods, including node-level and graph-level GNNs, by 12.4% over the strongest baseline. SUB-GNN performs exceptionally well on challenging biomedical datasets when subgraphs have complex topology and even comprise multiple disconnected components.