arXiv subjects

Joshua Lockhart

Publications and source records attributed to Joshua Lockhart.

18 recordsLinked to original sources

arXiv2022

Learn to explain yourself, when you can: Equipping Concept Bottleneck Models with the ability to abstain on their concept predictions

The Concept Bottleneck Models (CBMs) of Koh et al. [2020] provide a means to ensure that a neural network based classifier bases its predictions solely on human understandable concepts. The concept labels, or rationales as we refer to them, are learned by the concept labeling component of the CBM. Another component learns to predict the target classification label from these predicted concept labels. Unfortunately, these models are heavily reliant on human provided concept labels for each datapoint. To enable CBMs to behave robustly when these labels are not readily available, we show how to equip them with the ability to abstain from predicting concepts when the concept labeling component is uncertain. In other words, our model learns to provide rationales for its predictions, but only whenever it is sure the rationale is correct.

cs.LG↗

arXiv2022

Towards learning to explain with concept bottleneck models: mitigating information leakage

Concept bottleneck models perform classification by first predicting which of a list of human provided concepts are true about a datapoint. Then a downstream model uses these predicted concept labels to predict the target label. The predicted concepts act as a rationale for the target prediction. Model trust issues emerge in this paradigm when soft concept labels are used: it has previously been observed that extra information about the data distribution leaks into the concept predictions. In this work we show how Monte-Carlo Dropout can be used to attain soft concept predictions that do not contain leaked information.

cs.LG↗

arXiv2022

Feature Importance for Time Series Data: Improving KernelSHAP

Feature importance techniques have enjoyed widespread attention in the explainable AI literature as a means of determining how trained machine learning models make their predictions. We consider Shapley value based approaches to feature importance, applied in the context of time series data. We present closed form solutions for the SHAP values of a number of time series models, including VARMAX. We also show how KernelSHAP can be applied to time series tasks, and how the feature importances that come from this technique can be combined to perform "event detection". Finally, we explore the use of Time Consistent Shapley values for feature importance.

cs.LG↗

arXiv2022

Reductive MDPs: A Perspective Beyond Temporal Horizons

Solving general Markov decision processes (MDPs) is a computationally hard problem. Solving finite-horizon MDPs, on the other hand, is highly tractable with well known polynomial-time algorithms. What drives this extreme disparity, and do problems exist that lie between these diametrically opposed complexities? In this paper we identify and analyse a sub-class of stochastic shortest path problems (SSPs) for general state-action spaces whose dynamics satisfy a particular drift condition. This construction generalises the traditional, temporal notion of a horizon via decreasing reachability: a property called reductivity. It is shown that optimal policies can be recovered in polynomial-time for reductive SSPs -- via an extension of backwards induction -- with an efficient analogue in reductive MDPs. The practical considerations of the proposed approach are discussed, and numerical verification provided on a canonical optimal liquidation problem.

cs.AI↗

arXiv2022

Asynchronous Collaborative Learning Across Data Silos

Machine learning algorithms can perform well when trained on large datasets. While large organisations often have considerable data assets, it can be difficult for these assets to be unified in a manner that makes training possible. Data is very often 'siloed' in different parts of the organisation, with little to no access between silos. This fragmentation of data assets is especially prevalent in heavily regulated industries like financial services or healthcare. In this paper we propose a framework to enable asynchronous collaborative training of machine learning models across data silos. This allows data science teams to collaboratively train a machine learning model, without sharing data with one another. Our proposed approach enhances conventional federated learning techniques to make them suitable for this asynchronous training in this intra-organisation, cross-silo setting. We validate our proposed approach via extensive experiments.

cs.LG↗

arXiv2021

Equivalent Laplacian and Adjacency Quantum Walks on Irregular Graphs

The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems, however, the Hamiltonian is proportional to the adjacency matrix instead. It is well-known that these quantum walks are equivalent when the graph is regular, i.e., when each vertex has the same number of neighbors. If the graph is irregular, however, the quantum walks evolve differently. In this paper, we show that for some irregular graphs, if the particle is initially localized at a certain vertex, the probability distributions of the two quantum walks are identical, even though the amplitudes differ. We analytically prove this for a graph with five vertices and a graph with six vertices. By simulating the walks on all 1,018,689,568 simple, connected, irregular graphs with eleven vertices or less, we found sixty-four graphs with this notion of equivalence. We also give eight infinite families of graphs supporting these equivalent walks.

quant-ph↗

arXiv2020

SURF: Improving classifiers in production by learning from busy and noisy end users

Supervised learning classifiers inevitably make mistakes in production, perhaps mis-labeling an email, or flagging an otherwise routine transaction as fraudulent. It is vital that the end users of such a system are provided with a means of relabeling data points that they deem to have been mislabeled. The classifier can then be retrained on the relabeled data points in the hope of performance improvement. To reduce noise in this feedback data, well known algorithms from the crowdsourcing literature can be employed. However, the feedback setting provides a new challenge: how do we know what to do in the case of user non-response? If a user provides us with no feedback on a label then it can be dangerous to assume they implicitly agree: a user can be busy, lazy, or no longer a user of the system! We show that conventional crowdsourcing algorithms struggle in this user feedback setting, and present a new algorithm, SURF, that can cope with this non-response ambiguity.

cs.LG↗

arXiv2020

Some people aren't worth listening to: periodically retraining classifiers with feedback from a team of end users

Document classification is ubiquitous in a business setting, but often the end users of a classifier are engaged in an ongoing feedback-retrain loop with the team that maintain it. We consider this feedback-retrain loop from a multi-agent point of view, considering the end users as autonomous agents that provide feedback on the labelled data provided by the classifier. This allows us to examine the effect on the classifier's performance of unreliable end users who provide incorrect feedback. We demonstrate a classifier that can learn which users tend to be unreliable, filtering their feedback out of the loop, thus improving performance in subsequent iterations.

cs.LG↗

arXiv2019

On the Importance of Opponent Modeling in Auction Markets

The dynamics of financial markets are driven by the interactions between participants, as well as the trading mechanisms and regulatory frameworks that govern these interactions. Decision-makers would rather not ignore the impact of other participants on these dynamics and should employ tools and models that take this into account. To this end, we demonstrate the efficacy of applying opponent-modeling in a number of simulated market settings. While our simulations are simplified representations of actual market dynamics, they provide an idealized "playground" in which our techniques can be demonstrated and tested. We present this work with the aim that our techniques could be refined and, with some effort, scaled up to the full complexity of real-world market scenarios. We hope that the results presented encourage practitioners to adopt opponent-modeling methods and apply them online systems, in order to enable not only reactive but also proactive decisions to be made.

q-fin.CP↗

arXiv2019

How to Evaluate Trading Strategies: Single Agent Market Replay or Multiple Agent Interactive Simulation?

We show how a multi-agent simulator can support two important but distinct methods for assessing a trading strategy: Market Replay and Interactive Agent-Based Simulation (IABS). Our solution is important because each method offers strengths and weaknesses that expose or conceal flaws in the subject strategy. A key weakness of Market Replay is that the simulated market does not substantially adapt to or respond to the presence of the experimental strategy. IABS methods provide an artificial market for the experimental strategy using a population of background trading agents. Because the background agents attend to market conditions and current price as part of their strategy, the overall market is responsive to the presence of the experimental strategy. Even so, IABS methods have their own weaknesses, primarily that it is unclear if the market environment they provide is realistic. We describe our approach in detail, and illustrate its use in an example application: The evaluation of market impact for various size orders.

q-fin.TR↗

arXiv2018

Quantum Walk Search on Kronecker Graphs

Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with real-world properties. In this paper, we explore spatial search by continuous-time quantum walk on Kronecker graphs. Specifically, we give analytical proofs for quantum search on first-, second-, and third-order Kronecker graphs with the complete graph as the initiator, showing that search takes Grover's $O(\sqrt{N})$ time. Numerical simulations indicate that higher-order Kronecker graphs with the complete initiator also support optimal quantum search.

quant-ph↗

arXiv2018

Hierarchical quantum classifiers

Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer.

quant-ph↗

arXiv2017

Quantum State Isomorphism

We consider a problem we call StateIsomorphism: given two quantum states of n qubits, can one be obtained from the other by rearranging the qubit subsystems? Our main goal is to study the complexity of this problem, which is a natural quantum generalisation of the problem StringIsomorphism. We show that StateIsomorphism is at least as hard as GraphIsomorphism, and show that these problems have a similar structure by presenting evidence to suggest that StateIsomorphism is an intermediate problem for QCMA. In particular, we show that the complement of the problem, StateNonIsomorphism, has a two message quantum interactive proof system, and that this proof system can be made statistical zero-knowledge. We consider also StabilizerStateIsomorphism (SSI) and MixedStateIsomorphism (MSI), showing that the complement of SSI has a quantum interactive proof system that uses classical communication only, and that MSI is QSZK-hard.

quant-ph↗

arXiv2017

Entanglement properties of quantum grid states

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way. With these ideas we find bound entangled grid states for two-particle systems of any dimension and multiparticle grid states that provide examples for the different aspects of genuine multiparticle entanglement. Our findings suggest that entanglement theory for grid states, although being a discrete set, has already a complexity similar to the one for general states.

quant-ph↗

arXiv2016

The Computational Complexity of Portal and Other 3D Video Games

We classify the computational complexity of the popular video games Portal and Portal 2. We isolate individual mechanics of the game and prove NP-hardness, PSPACE-completeness, or (pseudo)polynomiality depending on the specific game mechanics allowed. One of our proofs generalizes to prove NP-hardness of many other video games such as Half-Life 2, Halo, Doom, Elder Scrolls, Fallout, Grand Theft Auto, Left 4 Dead, Mass Effect, Deus Ex, Metal Gear Solid, and Resident Evil. These results build on the established literature on the complexity of video games.

cs.CC↗

arXiv2016

Note on von Neumann and R\'enyi entropies of a Graph

We conjecture that all connected graphs of order $n$ have von Neumann entropy at least as great as the star $K_{1,n-1}$ and prove this for almost all graphs of order $n$. We show that connected graphs of order $n$ have R\'enyi 2-entropy at least as great as $K_{1,n-1}$ and for $\alpha>1$, $K_n$ maximizes R\'enyi $\alpha$-entropy over graphs of order $n$. We show that adding an edge to a graph can lower its von Neumann entropy.

math.CO↗

arXiv2016

Combinatorial Entanglement

We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to emit a particular quantum state on demand, but which can make an error and emit a different one. The device is able to produce a list of candidate states which can be used as a kind of debugging information for testing entanglement. By reformulating the Peres-Horodecki and matrix realignment criteria we are able to capture some characteristic features of entanglement: we construct new bound entangled states, and demonstrate the limitations of matrix realignment. We show how the notion of LOCC is related to a generalisation of the graph isomorphism problem. We give a simple proof that asymptotically almost surely, grid-labelled graphs associated to very sparse density matrices are entangled. We develop tools for enumerating grid-labelled graphs that satisfy the Peres-Horodecki criterion up to a fixed number of vertices, and propose various computational problems for these objects, whose complexity remains an open problem. The proposed mathematical framework also suggests new combinatorial and algebraic ways for describing the structure of graphs.

quant-ph↗

arXiv2015

Discrete-time quantum walks as generators of multipartite entanglement

We extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time step between the walker and the vertex qubits generates multipartite entanglement between the qubits. We demonstrate that for particular coin operators the system generates a highly entangled cluster state, of use in measurement based quantum computation.

quant-ph↗