Jia He

He Jia, Hong-Ming Zhu, Ue-Li Pen

The angular momentum of galaxies (galaxy spin) contains rich information about the initial condition of the Universe, yet it is challenging to efficiently measure the spin direction for the tremendous amount of galaxies that are being mapped by the ongoing and forthcoming cosmological surveys. We present a machine learning based classifier for the Z-wise vs S-wise spirals, which can help to break the degeneracy in the galaxy spin direction measurement. The proposed Chirality Equivariant Residual Network (CE-ResNet) is manifestly equivariant under a reflection of the input image, which guarantees that there is no inherent asymmetry between the Z-wise and S-wise probability estimators. We train the model with Sloan Digital Sky Survey (SDSS) images, with the training labels given by the Galaxy Zoo 1 (GZ1) project. A combination of data augmentation tricks are used during the training, making the model more robust to be applied to other surveys. We find a $\sim\!30\%$ increase of both types of spirals when Dark Energy Spectroscopic Instrument (DESI) images are used for classification, due to the better imaging quality of DESI. We verify that the $\sim\!7σ$ difference between the numbers of Z-wise and S-wise spirals is due to human bias, since the discrepancy drops to $<\!1.8σ$ with our CE-ResNet classification results. We discuss the potential systematics that are relevant to the future cosmological applications.

He Jia, Pravesh K . Kothari, Santosh S. Vempala

We present a polynomial-time algorithm for robustly learning an unknown affine transformation of the standard hypercube from samples, an important and well-studied setting for independent component analysis (ICA). Specifically, given an $ε$-corrupted sample from a distribution $D$ obtained by applying an unknown affine transformation $x \rightarrow Ax+s$ to the uniform distribution on a $d$-dimensional hypercube $[-1,1]^d$, our algorithm constructs $\hat{A}, \hat{s}$ such that the total variation distance of the distribution $\hat{D}$ from $D$ is $O(ε)$ using poly$(d)$ time and samples. Total variation distance is the information-theoretically strongest possible notion of distance in our setting and our recovery guarantees in this distance are optimal up to the absolute constant factor multiplying $ε$. In particular, if the columns of $A$ are normalized to be unit length, our total variation distance guarantee implies a bound on the sum of the $\ell_2$ distances between the column vectors of $A$ and $A'$, $\sum_{i =1}^d \|a_i-\hat{a}_i\|_2 = O(ε)$. In contrast, the strongest known prior results only yield a $ε^{O(1)}$ (relative) bound on the distance between individual $a_i$'s and their estimates and translate into an $O(dε)$ bound on the total variation distance. Our key innovation is a new approach to ICA (even to outlier-free ICA) that circumvents the difficulties in the classical method of moments and instead relies on a new geometric certificate of correctness of an affine transformation. Our algorithm is based on a new method that iteratively improves an estimate of the unknown affine transformation whenever the requirements of the certificate are not met.

Feiyang Pan, Tongzhe Zhang, Ling Luo et al.

Optimal execution is a sequential decision-making problem for cost-saving in algorithmic trading. Studies have found that reinforcement learning (RL) can help decide the order-splitting sizes. However, a problem remains unsolved: how to place limit orders at appropriate limit prices? The key challenge lies in the "continuous-discrete duality" of the action space. On the one hand, the continuous action space using percentage changes in prices is preferred for generalization. On the other hand, the trader eventually needs to choose limit prices discretely due to the existence of the tick size, which requires specialization for every single stock with different characteristics (e.g., the liquidity and the price range). So we need continuous control for generalization and discrete control for specialization. To this end, we propose a hybrid RL method to combine the advantages of both of them. We first use a continuous control agent to scope an action subset, then deploy a fine-grained agent to choose a specific limit price. Extensive experiments show that our method has higher sample efficiency and better training stability than existing RL algorithms and significantly outperforms previous learning-based methods for order execution.

Dapeng Li, Feiyang Pan, Jia He et al.

In high-dimensional time-series analysis, it is essential to have a set of key factors (namely, the style factors) that explain the change of the observed variable. For example, volatility modeling in finance relies on a set of risk factors, and climate change studies in climatology rely on a set of causal factors. The ideal low-dimensional style factors should balance significance (with high explanatory power) and stability (consistent, no significant fluctuations). However, previous supervised and unsupervised feature extraction methods can hardly address the tradeoff. In this paper, we propose Style Miner, a reinforcement learning method to generate style factors. We first formulate the problem as a Constrained Markov Decision Process with explanatory power as the return and stability as the constraint. Then, we design fine-grained immediate rewards and costs and use a Lagrangian heuristic to balance them adaptively. Experiments on real-world financial data sets show that Style Miner outperforms existing learning-based methods by a large margin and achieves a relatively 10% gain in R-squared explanatory power compared to the industry-renowned factors proposed by human experts.

Jingyi Yang, Zitong Yu, Xiuming Ni et al.

In videos containing spoofed faces, we may uncover the spoofing evidence based on either photometric or dynamic abnormality, even a combination of both. Prevailing face anti-spoofing (FAS) approaches generally concentrate on the single-frame scenario, however, purely photometric-driven methods overlook the dynamic spoofing clues that may be exposed over time. This may lead FAS systems to conclude incorrect judgments, especially in cases where it is easily distinguishable in terms of dynamics but challenging to discern in terms of photometrics. To this end, we propose the Graph Guided Video Vision Transformer (G$^2$V$^2$former), which combines faces with facial landmarks for photometric and dynamic feature fusion. We factorize the attention into space and time, and fuse them via a spatiotemporal block. Specifically, we design a novel temporal attention called Kronecker temporal attention, which has a wider receptive field, and is beneficial for capturing dynamic information. Moreover, we leverage the low-semantic motion of facial landmarks to guide the high-semantic change of facial expressions based on the motivation that regions containing landmarks may reveal more dynamic clues. Extensive experiments on nine benchmark datasets demonstrate that our method achieves superior performance under various scenarios. The codes will be released soon.

He Jia

We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. Posterior samples are obtained by interpolating the predicted quantiles using monotonic cubic Hermite spline, with specific treatment for the tail behavior and multi-modal distributions. We introduce an alternative definition for the Bayesian credible region using the local Cumulative Density Function (CDF), offering substantially faster evaluation than the traditional Highest Posterior Density Region (HPDR). In case of limited simulation budget and/or known model misspecification, a post-processing calibration step can be integrated into NQE to ensure the unbiasedness of the posterior estimation with negligible additional computational cost. We demonstrate that NQE achieves state-of-the-art performance on a variety of benchmark problems.

He Jia

A major challenge in extracting information from current and upcoming surveys of cosmological Large-Scale Structure (LSS) is the limited availability of computationally expensive high-fidelity simulations. We introduce Neural Quantile Estimation (NQE), a new Simulation-Based Inference (SBI) method that leverages a large number of approximate simulations for training and a small number of high-fidelity simulations for calibration. This approach guarantees an unbiased posterior and achieves near-optimal constraining power when the approximate simulations are reasonably accurate. As a proof of concept, we demonstrate that cosmological parameters can be inferred at field level from projected 2-dim dark matter density maps up to $k_{\rm max}\sim1.5\,h$/Mpc at $z=0$ by training on $\sim10^4$ Particle-Mesh (PM) simulations with transfer function correction and calibrating with $\sim10^2$ Particle-Particle (PP) simulations. The calibrated posteriors closely match those obtained by directly training on $\sim10^4$ expensive PP simulations, but at a fraction of the computational cost. Our method offers a practical and scalable framework for SBI of cosmological LSS, enabling precise inference across vast volumes and down to small scales.

Shuo Yu, Hongyan Xue, Xiang Ao et al.

In the field of quantitative trading, it is common practice to transform raw historical stock data into indicative signals for the market trend. Such signals are called alpha factors. Alphas in formula forms are more interpretable and thus favored by practitioners concerned with risk. In practice, a set of formulaic alphas is often used together for better modeling precision, so we need to find synergistic formulaic alpha sets that work well together. However, most traditional alpha generators mine alphas one by one separately, overlooking the fact that the alphas would be combined later. In this paper, we propose a new alpha-mining framework that prioritizes mining a synergistic set of alphas, i.e., it directly uses the performance of the downstream combination model to optimize the alpha generator. Our framework also leverages the strong exploratory capabilities of reinforcement learning~(RL) to better explore the vast search space of formulaic alphas. The contribution to the combination models' performance is assigned to be the return used in the RL process, driving the alpha generator to find better alphas that improve upon the current set. Experimental evaluations on real-world stock market data demonstrate both the effectiveness and the efficiency of our framework for stock trend forecasting. The investment simulation results show that our framework is able to achieve higher returns compared to previous approaches.

Ainesh Bakshi, Ilias Diakonikolas, He Jia et al.

We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. This resolves the main open problem in several previous works on algorithmic robust statistics, which addressed the special cases of robustly estimating (a) a single Gaussian, (b) a mixture of TV-distance separated Gaussians, and (c) a uniform mixture of two Gaussians. Our main tools are an efficient \emph{partial clustering} algorithm that relies on the sum-of-squares method, and a novel \emph{tensor decomposition} algorithm that allows errors in both Frobenius norm and low-rank terms.