AI 中文总结
本文比较了两种基于最小二乘的时间序列预测方法，发现预测程序在标量目标下与普通最小二乘等价，并在特定四维序列上优于向量拟合，秩2时两者一致。
AI 中文摘要
时间序列预测是根据序列的未来值进行评分的。如LeNEPA中那样，对下一个潜在变量进行回归的表示损失，是在同一瓶颈上的一个不同的最小二乘问题。我们将这两个问题都写下来。预测程序最小化解码潜在变量在将要报告的坐标上的误差。对于标量目标和线性解码器，每个至少为1的潜在秩与普通最小二乘匹配，并且各向同性约束仅是一种重新缩放：在重新拟合解码器后，预测不会移动。另一个程序在固定秩下拟合整个下一个向量，然后冻结编码器并附加一个预测头。在一个四维序列上，其最后三个坐标是相同的自回归，该秩1拟合将质量0.9998放在重复坐标上，并以边际方差2.794预测剩余信号。预测程序将质量1放在信号上，并匹配创新方差0.992。秩2为向量拟合提供了第二个方向，两个程序达成一致。迭代拟合的一步系数0.803将开环误差从一步时的0.992提高到八步时的2.700。
英文摘要
A time-series forecast is scored on a future value of the series. A representation loss that regresses the next latent, as in LeNEPA, is a different least-squares problem on the same bottleneck. We write both programs down. The forecast program minimizes the error of a decoded latent on the coordinate that will be reported. For a scalar target and a linear decoder, every latent rank of at least one matches ordinary least squares, and an isotropy constraint is only a rescaling: after the decoder is refit, the forecast does not move. The other program fits the whole next vector at a fixed rank, then freezes the encoder and attaches a head. On a four-dimensional series whose last three coordinates are the same autoregression, that rank-1 fit puts mass $0.9998$ on the repeated coordinate and forecasts the remaining signal at the marginal variance $2.794$. The forecast program puts mass $1$ on the signal and matches the innovation variance $0.992$. Rank $2$ gives the vector fit a second direction, and the two programs agree. Iterating the fitted one-step coefficient $0.803$ raises the open-loop error from $0.992$ at one step to $2.700$ at eight steps.
Comments20 pages, 2 figures
