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<footnote n="1">¹ INAF – Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy</footnote>

<footnote n="2">² Departmento de Inteligencia Artificial, UNED, c/ Juan del Rosal 16, 28040 Madrid, Spain</footnote>

<footnote n="3">³ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany</footnote>

<footnote n="4">⁴ Institut UTINAM CNRS UMR6213, Université Bourgogne Franche-Comté, OSU THETA Franche-Comté Bourgogne, Observatoire de Besançon, BP1615, 25010 Besançon Cedex, France</footnote>

<footnote n="5">⁵ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK</footnote>

<footnote n="6">⁶ School of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK</footnote>

<footnote n="7">⁷ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201AZ, Noordwijk, The Netherlands</footnote>

<footnote n="8">⁸ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain</footnote>

<footnote n="9">⁹ Centre for Astrophysics Research, University of Hertfordshire, College Lane, AL10 9AB, Hatfield, UK</footnote>

<footnote n="10">¹⁰ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK</footnote>

<footnote n="11">¹¹ RHEA for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain</footnote>

<footnote n="12">¹² Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands</footnote>

<footnote n="13">¹³ INAF – Osservatorio astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy</footnote>

<footnote n="14">¹⁴ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France</footnote>

<footnote n="15">¹⁵ GEPI, Observatoire de Paris, Université PSL, CNRS, 5 Place Jules Janssen, 92190 Meudon, France</footnote>

<footnote n="16">¹⁶ Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr. 12-14, 69120 Heidelberg, Germany</footnote>

<footnote n="17">¹⁷ Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France</footnote>
18 Department of Astronomy, University of Geneva, Chemin des Mail-lettres 51, 1290 Versoix, Switzerland

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123 Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton NJ 08544, USA

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125 naXys, University of Namur, Rempart de la Vierge, 5000 Namur, Belgium

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127 H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK

128 Sorbonne Université, CNRS, UMR7095, Institut d'Astrophysique de Paris, 98bis bd. Arago, 75014 Paris, France

129 Porter School of the Environment and Earth Sciences, Tel Aviv University, Tel Aviv 6997801, Israel

130 Laboratoire Univers et Particules de Montpellier, Université Montpellier, Place Eugène Bataillon, CC72, 34095 Montpellier Cedex 05, France

131 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
# Appendix A: Details of the random forest classifier parameters and training set.

<figure><img src="image_41.png" /><figcaption>**Fig. A.1.** CAMD with colour $G-G_{RP}$ and absolute magnitude $M_G$ of the set of sources with parallaxes greater than or equal to 8 mas (black) and those used as examples of good astrometry (red points) in the random forest training set.</figcaption></figure>

<figure><img src="image_42.png" /><figcaption>**Fig. A.2.** As Fig. A.1 for $M_G$ and the 2MASS colour index $J-H$.</figcaption></figure>

## A.1. Colour-absolute magnitude diagrams

Figures A.1–A.3 show the position in several colour-absolute magnitude diagrams of the sources selected as examples of good astrometry in the training set (red) superimposed on the full distribution of sources with observed parallaxes greater than or equal to 8 mas. Figures A.3 and A.2 show that the requirement to have a 2MASS counterpart to the Gaia source already removes most of the sources with spurious observed parallaxes greater than 8 mas.

<figure><img src="image_43.png" /><figcaption>**Fig. A.3.** As Fig. A.1 for $M_J$ and the $G-H$ colour index.</figcaption></figure>

<figure><img src="image_44.png" /><figcaption>**Fig. A.4.** Distribution of values of the parallax_error feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).</figcaption></figure>

## A.2. Parameters tested for relevance

Table A.1 lists all catalogue columns tested for relevance in the classification problem of separating good astrometric solutions from spurious ones. We did not check for the relevance of astrometric_primary_flag, astrometric_weight_ac", nu eff_used_in.astrometry, pseudocolour, and pseudocolour_error due to the high fraction of missing values in the training set.
### A.3. Distributions of features

<table><caption>**Table A.1.** Importance of all features tested for classification by the Random Forest classifier ordered according to the mean decrease in accuracy (two leftmost columns) and by the mean decrease in the Gini index (two rightmost columns).</caption><thead><tr><th>Feature name</th><th>Mean decrease accuracy</th><th>Feature name</th><th>Mean decrease Gini index</th></tr></thead><tbody><tr><td>parallax_error</td><td>0.125</td><td>parallax_error</td><td>33821</td></tr><tr><td>parallax_over_error</td><td>0.087</td><td>parallax_over_error</td><td>27713</td></tr><tr><td>pmra</td><td>0.056</td><td>astrometricsigma5d_max</td><td>24035</td></tr><tr><td>astrometricsigma5d_max</td><td>0.052</td><td>pmra_error</td><td>20226</td></tr><tr><td>pmdec</td><td>0.047</td><td>pmdec_error</td><td>14866</td></tr><tr><td>pmdec_error</td><td>0.027</td><td>astrometricexcess-noise</td><td>12737</td></tr><tr><td>pmra_error</td><td>0.025</td><td>astrometric_params_solved</td><td>7677</td></tr><tr><td>astrometricexcess-noise</td><td>0.013</td><td>ipd_gof_harmonic_amplitude</td><td>5628</td></tr><tr><td>visibility periods used</td><td>0.01</td><td>ruwe</td><td>3383</td></tr><tr><td>ruwe</td><td>0.008</td><td>visibility periods used</td><td>2371</td></tr><tr><td>astrometric gof al</td><td>0.005</td><td>pmdec</td><td>2263</td></tr><tr><td>astrometricnobs ac</td><td>0.005</td><td>pmra</td><td>2039</td></tr><tr><td>ipd gof_harmonic_amplitude</td><td>0.004</td><td>ipdfrac odd win</td><td>1566</td></tr><tr><td>astrometricexcess-noise sig</td><td>0.003</td><td>ipdfrac multi peak</td><td>1006</td></tr><tr><td>ipdfrac odd win</td><td>0.002</td><td>astrometric gof al</td><td>801</td></tr><tr><td>astrometric chi2 al</td><td>0.002</td><td>scan direction strength k2</td><td>694</td></tr><tr><td>parallax pmdec corr</td><td>0.002</td><td>parallax pmdec corr</td><td>522</td></tr><tr><td>ipdfrac multi peak</td><td>0.002</td><td>astrometricexcess-noise sig</td><td>413</td></tr><tr><td>scan direction strength k2</td><td>0.001</td><td>astrometricn good obs al</td><td>394</td></tr><tr><td>astrometricn good obs al</td><td>0.001</td><td>astrometric chi2 al</td><td>275</td></tr><tr><td>astrometric_params_solved</td><td>0.001</td><td>astrometricn obs al</td><td>244</td></tr><tr><td>astrometricn obs al</td><td>0.001</td><td>astrometricn obs ac</td><td>224</td></tr><tr><td>astrometric matched transits</td><td>0.001</td><td>dec parallax corr</td><td>208</td></tr><tr><td>dec parallax corr</td><td>0.001</td><td>astrometric matched transits</td><td>165</td></tr><tr><td>dec pmdec corr</td><td>0.001</td><td>dec pmdec corr</td><td>157</td></tr><tr><td>scan direction mean k2</td><td>0.001</td><td>ra dec corr</td><td>65</td></tr><tr><td>ra parallax corr</td><td>0</td><td>scan direction strength k1</td><td>59</td></tr><tr><td>scan direction strength k4</td><td>0</td><td>scan direction mean k2</td><td>50</td></tr><tr><td>ra dec corr</td><td>0</td><td>scan direction strength k4</td><td>50</td></tr><tr><td>scan direction strength k1</td><td>0</td><td>parallax pmra corr</td><td>49</td></tr><tr><td>scan direction mean k4</td><td>0</td><td>ra parallax corr</td><td>48</td></tr><tr><td>scan direction strength k3</td><td>0</td><td>ra pmdec corr</td><td>44</td></tr><tr><td>parallax pmra corr</td><td>0</td><td>scan direction mean k4</td><td>42</td></tr><tr><td>astrometricn bad obs al</td><td>0</td><td>scan direction strength k3</td><td>41</td></tr><tr><td>ra pmdec corr</td><td>0</td><td>astrometricn bad obs al</td><td>38</td></tr><tr><td>scan direction mean k3</td><td>0</td><td>scan direction mean k3</td><td>30</td></tr><tr><td>ipd gof_harmonic phase</td><td>0</td><td>ipd gof_harmonic phase</td><td>29</td></tr><tr><td>pmra pmdec corr</td><td>0</td><td>ra pmra corr</td><td>28</td></tr><tr><td>scan direction mean k1</td><td>0</td><td>pmra pmdec corr</td><td>27</td></tr><tr><td>ra pmra corr</td><td>0</td><td>scan direction mean k1</td><td>24</td></tr><tr><td>dec pmra corr</td><td>0</td><td>dec pmra corr</td><td>22</td></tr></tbody></table>
<figure><img src="image_45.png" /></figure>

**Fig. A.5.** Distribution of values of the parallax_over_error feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_46.png" /></figure>

**Fig. A.7.** Distribution of values of the pmra_error feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_47.png" /></figure>

**Fig. A.6.** Distribution of values of the astrometricsigma5d_max feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_48.png" /></figure>

**Fig. A.8.** Distribution of values of the pmdec_error feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).
<figure><img src="image_49.png" /></figure>

**Fig. A.9.** Distribution of values of the astrometric_excess_noise feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_50.png" /></figure>

**Fig. A.10.** Distribution of values of the ipd_gof_harmonic_amplitude feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_51.png" /></figure>

**Fig. A.11.** Distribution of values of the ruwe feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_52.png" /></figure>

**Fig. A.12.** Distribution of values of the visibility períods_used feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).
<figure><img src="image_53.png" /></figure>

**Fig. A.13.** Distribution of values of the pmdec feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_54.png" /></figure>

**Fig. A.15.** Distribution of values of the ipd FracOdd win feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_55.png" /></figure>

**Fig. A.14.** Distribution of values of the pmra feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).

<figure><img src="image_56.png" /></figure>

**Fig. A.16.** Distribution of values of the ipd FracMulti_peak feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).
<figure><img src="image_57.png" /><figcaption>Fig. A.17. Distribution of values of the astrometric_gof_al feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).</figcaption></figure>

<figure><img src="image_58.png" /><figcaption>Fig. A.18. Distribution of values of the scan_direction_strength_k2 feature in the set of training examples of the bad category (continuous line, white filling); in the set of training examples of the good category (dotted line, white filling); the set of sources classified as bad astrometric solutions (dashed line, blue transparent filling); and the set of sources classified as good astrometric solutions (dash-dotted line, red transparent filling).</figcaption></figure>

## Appendix B: The relations and Gaussian Mixture Model priors used for the determination of space velocities in Galactic coordinates

The relations that define space velocities in terms of the observables, Gaia coordinates, parallaxes and proper motions, and radial velocities are:

$$ \begin{pmatrix} u \\ v \\ w \end{pmatrix} = A_G^T \cdot A \cdot \begin{pmatrix} 4.74047 \mu_{\alpha} / \varpi \\ 4.74047 \mu_{\delta} / \varpi \\ v_r \end{pmatrix} \qquad (B.1) $$

where $A_G$ is the transformation matrix to Galactic coordinates from the introduction to the HIPPARCOS catalogue (ESA 1997) and matrix A is obtained from the components of the normal triad at the star as:

$$ A = \begin{pmatrix} -\sin\alpha & -\sin\delta\cos\alpha & \cos\delta\cos\alpha \\ \cos\alpha & -\sin\delta\sin\alpha & \cos\delta\sin\alpha \\ 0 & \cos\delta & \sin\delta \end{pmatrix} \qquad (B.2) $$

The Bayesian model used to infer posterior probabilities for the space velocities requires the definition of priors for the model parameters. As described in Sect. 3, we fit Gaussian Mixture Models to a local (140 pc) simulation from the Besançon Galaxy model (Robin et al. 2003) and modify the result by adding a wide non-informative component. The resulting priors used in the inference process are defined in Eqs. (B.3)–(B.5) using the notation $N(\cdot | \mu, \sigma)$ to denote the Gaussian distribution centred at $\mu$ and with standard deviation $\sigma$.

$$ \pi(U) = 0.52 \cdot N(U | -11.3, 23.2) \\ + 0.45 \cdot N(U | -11, 44) \\ + 0.03 \cdot N(U | 0, 120) \qquad (B.3) $$

$$ \pi(V) = 0.588 \cdot N(V | -26.1, 23.7) \\ + 0.375 \cdot N(V | -13, 11.3) \\ + 0.03 \cdot N(V | 0, 120) \\ + 0.007 \cdot N(V | -115.8, 114.3) \qquad (B.4) $$

$$ \pi(W) = 0.53 \cdot N(W | -7.3, 19.4) \\ + 0.2 \cdot N(W | -10, 9.2) \\ + 0.21 \cdot N(W | -4.1, 10.1) \\ + 0.03 \cdot N(W | -7, 43.3) \\ + 0.03 \cdot N(W | 0, 120) \qquad (B.5) $$